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b(is)i(an)e(in)m(tensional)k(mo)s(del?)0 321 y 1947 2 v 217 x fj(Meaning)30 b(of)f(a)f(program)f(could)j(b)r(e:)40 683 y fh(\017)21 b fj(a)29 b(function)h(on)e(a)h(ric)n(her)g(domain)f(than)h(in)104 787 y(exte\ nsional)i(seman)n(tics,)e(whose)g(structure)g(p)s(ermits)104 891 y(us)f(to)h (deduce)g(information)h(ab)r(out)f(computation)104 995 y(strategy)h([Colson,) f(Bro)s(ok)n(es)g(&)f(Gev)-5 b(a])40 1140 y fh(\017)21 b fj(a)29 b(pair)g(con\ sisting)i(of)e(a)f(function)j(and)d(an)h(ob)t(ject)104 1244 y(con)n(v)n(eying) h(in)n(tensional)h(information;)f(this)f(ob)5 b(ject)104 1348 y(could)29 b (represen)n(t)g(the)g(cost)h(of)f(ev)-5 b(aluating)32 b(the)104 1451 y(functi\ on,)e(or)e(could)i(b)r(e)f(a)g(function)h(from)e(inputs)h(to)104 1555 y(costs) g([Gurr,)f(Rosendahl])40 1701 y fh(\017)21 b fj(an)28 b(algorithm)i([Berry)f (&)f(Curien])958 2748 y fe(2)p eop %%Page: 3 4 bop 25 170 a fk(Outline)0 321 y 1947 2 v -450 6990 a @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: outline.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.62069 0 0 0.62069 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 218 1233 ] concat [ (CDS0) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 192 1220 ] concat [ ([Berry & Curien]) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 175 1206 ] concat [ (first intensional model) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 102 1166 ] concat [ (parallel algos) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 89 1151 ] concat [ ([Brookes & Geva]) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 183 1073 ] concat [ (circuit semantics) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 164 1058 ] concat [ ([Brookes & Dancanet]) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 164 1043 ] concat [ (relative intensional) (expressiveness comparisons) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 118 986 ] concat [ (deterministic) (extensions of PCF) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 258 986 ] concat [ (deterministic and) (nondeterministic) (extensions of PCF) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 318 1166 ] concat [ (applications) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 278 1135 ] concat [ ([Hughes et al]) (loop detection) (abstract interp) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 389 1135 ] concat [ ([Dancanet]) (intensional types) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1 0 0 1 69.75 672 ] concat 73 499 170 516 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1 0 0 1 69 672 ] concat 171 516 286 500 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1 0 0 1 69.75 671 ] concat 285 481 251 469 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1 0 0 1 69 672 ] concat 286 480 356 470 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1 0 0 1 69 672 ] concat 171 516 171 409 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1.02265 0 0 1 65.8932 671.75 ] concat 170 343 93 319 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 1 0 0 1 69 672 ] concat 171 343 242 319 Line End End %I eop showpage end %%EndDocument @endspecial 958 2748 a fe(3)p eop %%Page: 4 5 bop 25 170 a fk(PCF)0 321 y 1947 2 v 40 521 a fh(\017)21 b fj(Simple)29 b (functional)i(programming)c(language)40 662 y fh(\017)21 b fj(T)n(yp)r(es:) 208 795 y ff(\033)32 b fj(:)14 b(:)g(=)24 b ff(o)k fh(j)h ff(\023)g fh(j)g ff (\033)757 789 y fh(!)858 795 y ff(\033)40 946 y fh(\017)21 b fj(Syn)n(tax:) 208 1078 y ff(M)37 b fj(:)14 b(:)h(=)24 b ff(c)29 b fh(j)f ff(x)h fh(j)g ff (\025x:)g(M)37 b fh(j)29 b ff(M)9 b(M)40 1229 y fh(\017)21 b fj(Constan)n(ts:) 228 1354 y fd(tt)36 b fj(:)43 b ff(o)228 1457 y fd(\013)k fj(:)c ff(o)228 1561 y(n)29 b fj(:)43 b ff(\023)569 b fj(\(the)30 b(in)n(tegers,)f ff(n)24 b fh (\025)g fj(0\))228 1665 y fd(isZer)l(o?)39 b fj(:)k ff(\023)653 1659 y fh(!) 754 1665 y ff(o)228 1769 y fj(+1)29 b(:)43 b ff(\023)479 1763 y fh(!)579 1769 y ff(\023)228 1873 y fh(\000)p fj(1)29 b(:)43 b ff(\023)479 1867 y fh(!)579 1873 y ff(\023)228 1976 y fh(\033)295 1989 y fc(o)355 1976 y fj(:)g ff(o)478 1970 y fh(!)579 1976 y ff(o)635 1970 y fh(!)735 1976 y ff(o)791 1970 y fh(!) 892 1976 y ff(o)e fj(\(b)r(o)s(olean)30 b(conditional\))228 2080 y fh(\033) 295 2093 y fc(\023)347 2080 y fj(:)43 b ff(o)470 2074 y fh(!)571 2080 y ff (\023)616 2074 y fh(!)716 2080 y ff(\023)761 2074 y fh(!)861 2080 y ff(\023) 84 b fj(\(in)n(teger)30 b(conditional\))228 2184 y ff(Y)278 2197 y fc(\033) 345 2184 y fj(:)43 b(\()p ff(\033)512 2178 y fh(!)613 2184 y ff(\033)s fj(\)) 713 2178 y fh(!)813 2184 y ff(\033)113 b fj(\(one)29 b(for)g(eac)n(h)g ff(\ \033)s fj(\))228 2288 y(=)g(:)43 b ff(\023)436 2282 y fh(!)536 2288 y ff(\023) 581 2282 y fh(!)681 2288 y ff(o)252 b fj(\(in)n(teger)30 b(equalit)n(y\))958 2748 y fe(4)p eop %%Page: 5 6 bop 25 170 a fk(PCF)39 b(and)g(full)j(abstraction)f(I)0 321 y 1947 2 v 40 538 a fh(\017)21 b fj(PCF)28 b(is)i(a)f(paradigmatic)g(sequen)n(tial)j(programmin\ g)104 642 y(language)40 787 y fh(\017)21 b fj(Op)r(erational)31 b(seman)n(tic\ s)e fh(\))f fj(observ)-5 b(ational)104 891 y(equiv)g(alence)40 1036 y fh(\017) 21 b fj(Denotational)31 b(seman)n(tics)e fh(\))g fj(equalit)n(y)i(of)104 1140 y(denotations)40 1285 y fh(\017)21 b fj(F)-7 b(ull)30 b(abstraction:)104 1389 y(observ)-5 b(ational)31 b(equiv)-5 b(ale)q(nce)32 b fh(,)c fj(equalit)n(y)k (of)104 1493 y(denotations)40 1638 y fh(\017)21 b fj(Standard)28 b(denotation\ al)k(mo)q(del)d(of)g(PCF)104 1742 y(\(con)n(tin)n(uous)g(functions)h(on)f(cp) r(o's\))h(is)f(not)g(fully)104 1846 y(abstract)958 2748 y fe(5)p eop %%Page: 6 7 bop 25 170 a fk(PCF)39 b(and)g(full)j(abstraction)f(I)s(I)0 321 y 1947 2 v 40 543 a fh(\017)21 b fj(\012)166 556 y fc(\034)225 543 y fj(=)j ff(Y)366 556 y fc(\034)401 543 y fj(\()p ff(\025f)5 b(:)29 b(f)9 b fj(\))40 688 y fh(\017)21 b fj(OR)-7 b(TEST)28 b(=)h ff(\025i:)g(\025f)t(:)58 b fg(if)29 b fj(\()p ff (f)39 b fd(tt)d fj(\012\))979 792 y(\()29 b fg(if)h fj(\()p ff(f)38 b fj(\012) 29 b fd(tt)8 b fj(\))1128 896 y(\()29 b fg(if)g fj(\()p ff(f)39 b fd(\013)18 b (\013)g fj(\))29 b(\012)g ff(i)p fj(\))1128 1000 y(\012)979 1103 y(\))979 1207 y(\012)40 1352 y fh(\017)21 b fj(OR)-7 b(TEST)28 b(0)h(is)h(op)r(erationally) i(equiv)-5 b(ale)q(n)n(t)31 b(to)104 1456 y(OR)-7 b(TEST)28 b(1)40 1602 y fh (\017)21 b(D)s fj([)-15 b([OR)-7 b(TEST])-14 b(])p fh(?)23 b fj(=)104 1705 y ff(\025v)s(:)28 b(\025)p fj(\010)p ff(:)58 b fj(if)30 b(\010)24 b(=)g ff(por) 31 b fj(then)e ff(v)j fj(else)e fh(?)40 1851 y(\017)21 b(D)s fj([)-15 b([OR) -7 b(TEST)29 b(0])-15 b(])24 b fh(6)p fj(=)g fh(D)s fj([)-15 b([OR)-7 b(TEST) 29 b(1])-14 b(])40 1996 y fh(\017)21 b ff(por)31 b fd(tt)7 b fh(?)24 b fj(=)g fd(tt)104 2100 y ff(por)31 b fh(?)p fd(tt)g fj(=)24 b fd(tt)104 2203 y ff(por) 31 b fd(\013)18 b(\013)42 b fj(=)24 b fd(\013)958 2748 y fe(6)p eop %%Page: 7 8 bop 25 170 a fk(Concrete)40 b(data)g(structures)0 321 y 1947 2 v 40 538 a fh (\017)21 b fj(A)28 b(cds)h(is)g(lik)n(e)i(a)e(record:)125 696 y fg({)21 b fj (cells)125 820 y fg({)g fj(v)-5 b(alues)125 945 y fg({)21 b fj(accessibili)q (t)o(y)32 b(\(enabling\))f(relation)40 1103 y fh(\017)21 b fj(Example:)38 b (BOOL)-191 7515 y @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: bool.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.62069 0 0 0.62069 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 154 1207 ] concat [ (B) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 14 SetF [ 1 0 0 1 272 1203 ] concat [ (tt, ff) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 17 659 ] concat 150 522 176 548 Rect End Begin %I BSpl 1 1 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -9 672 ] concat 209 524 247 537 273 522 3 BSpl End End %I eop showpage end %%EndDocument @endspecial 40 1612 a fh(\017)21 b fj(Ev)n(en)n(t:)38 b(cell)31 b(=)d(v)-5 b (alue)40 1757 y fh(\017)21 b fj(State:)39 b fh(f)p ff(c)442 1770 y fe(1)498 1757 y fj(=)24 b ff(v)631 1770 y fe(1)663 1757 y ff(;)14 b(c)738 1770 y fe (2)794 1757 y fj(=)24 b ff(v)927 1770 y fe(2)959 1757 y ff(;)14 b(:)g(:)h(:)o fh(g)40 1903 y(\017)21 b fj(Example:)104 2007 y(States)30 b(of)f(BOOL)f(=)h fh (ffg)p ff(;)14 b fh(f)p ff(B)29 b fj(=)24 b fd(tt)7 b fh(g)p ff(;)14 b fh(f)p ff(B)29 b fj(=)24 b fd(\013)18 b fh(gg)958 2748 y fe(7)p eop %%Page: 8 9 bop 25 160 a fk(Sequen)m(tial)42 b(functions)0 321 y 1947 2 v 40 543 a fh (\017)21 b ff(F)12 b fj(\()p ff(x)p fj(\))25 b(=)k(cells)i(\014lled)f(in)g (state)g ff(x)40 688 y fh(\017)21 b ff(A)p fj(\()p 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b(and)g(circuits)j(1)0 321 y 1947 2 v 40 537 a fk(\ \017)21 b fl(W)-7 b(e)29 b(view)i(PCF)d(programs)f(as)i(circuits:)-299 6645 y @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: ../drawings/basic3.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.923077 0 0 0.923077 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict Begin %I Pict [ 1 0 0 1 60 207 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 127 465 ] concat 74 38 144 88 Rect End Begin %I Pict [ 1 0 0 1 -83.5 -77.5 ] concat Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 98 428 ] concat 323 300 333 300 347 292 333 284 322 284 5 BSpl End Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 92.5 428.5 ] concat 358 287 357 276 364 276 3 BSpl End End %I eop End %I eop Begin %I Pict [ 1 0 0 1 0 17.5 ] concat Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 220.5 738 ] concat [ (b) ] Text End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 238.5 738 ] concat [ (x) ] Text End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 260.5 738 ] concat [ (y) ] Text End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 178 511 ] concat 111 411 92 430 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 178 511 ] concat 128 410 128 464 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 178 511 ] concat 143 411 162 430 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 178 511 ] concat 128 360 128 324 Line End Begin %I Pict [ 1 0 0 1 -86 52 ] concat Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 167.5 664 ] concat [ (M) ] Text End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 170 703 ] concat [ (x) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 97 131 ] concat 76 560 76 542 Line End Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 97 131 ] concat 50 542 102 542 76 508 50 542 4 Poly End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 127 465 ] concat 92 348 92 314 Line End End %I eop Begin %I Pict [ 1 0 0 1 -129 52 ] concat Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 289.5 664 ] concat [ (M) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 219 131 ] concat 76 560 76 542 Line End Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 219 131 ] concat 50 542 102 542 76 508 50 542 4 Poly End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 249 465 ] concat 92 348 92 314 Line End Begin %I Pict [ 1 0 0 1 1 1.5 ] concat Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 127 456 ] concat 298 504 368 504 334 468 298 504 4 Poly End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 127 456 ] concat 334 504 334 520 Line End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 290 704.5 ] concat [ (N) ] Text End End %I eop End %I eop Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 80 656 ] concat [ (\(a\)) ] Text End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 160 656 ] concat [ (\(b\)) ] Text End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 236 656 ] concat [ (\(c\)) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 69 502 ] concat 310 448 310 482 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 69 502 ] concat 380 448 380 482 Line End End %I eop End %I eop showpage end %%EndDocument @endspecial 244 1888 a(\(a\))g fi(\025x:)g(M)9 b fl(,)29 b(\(b\))g(\()p fi (\025x:)h(M)9 b fl(\))p fi(N)h fl(,)28 b(\(c\))i fk(\033)1467 1901 y ff(\023) 1514 1888 y fi(b)f(x)g(y)40 2046 y fk(\017)21 b fl(Seman)n(tics)27 b(of)h(cir\ cuits)i(based)d(on)g(PCF's)g(op)s(erational)104 2150 y(seman)n(tics)944 2748 y fh(14)p eop %%Page: 15 16 bop 25 170 a fm(PCF)39 b(and)g(circuits)j(2)0 321 y 1947 2 v 40 538 a fk(\ \017)21 b fl(A)28 b(circuit)j(is)f fg(static)j fl(if)d(it)g(represen)n(ts)e (a)h(non-recursiv)n(e)104 642 y(PCF)f(program)40 787 y fk(\017)21 b fl(A)28 b (circuit)j(is)f fg(dynamic)k fl(if)c(it)g(represen)n(ts)f(a)f(recursiv)n(e) 104 891 y(PCF)g(program)40 1036 y fk(\017)21 b fl(The)29 b fg(depth)34 b fl (of)29 b(a)g(static)i(circuit)g(is)f(equal)g(to)f(the)104 1140 y(heigh)n(t)g (of)h(the)f(underlying)h(tree)40 1285 y fk(\017)21 b fl(A)28 b(circuit)j(is)f fg(c)l(onstant-depth)j fl(if)d(it)g(is)g(either)g(static,)104 1389 y(or)e(a)h (dynamic)g(circuit)i(whic)n(h)e(do)r(es)g(not)g(expand)104 1493 y(more)e(than) i(a)g(\014xed)g(constan)n(t)g(n)n(um)n(ber)g(of)g(times)104 1597 y(\(indep)s (enden)n(t)g(of)g(the)g(inputs\))40 1742 y fk(\017)21 b fl(If)29 b(t)n(w)n (o)f(functions)j(can)d(b)s(e)h(implemen)n(ted)f(in)i(terms)d(of)104 1846 y (eac)n(h)h(other)i(with)g(constan)n(t-depth)f(circuits,)i(w)n(e)e(sa)n(y)104 1950 y(that)g(the)h(t)n(w)n(o)e(functions)i(are)f fg(intensional)6 b(ly)104 2053 y(e)l(quivalent)944 2748 y fh(15)p eop %%Page: 16 17 bop 25 170 a fm(P)m(arallel)42 b(extensions)g(of)e(PCF)0 321 y 1947 2 v 40 538 a fk(\017)21 b fl(P)n(arallel-or:)104 642 y fi(por)31 b fl(:)43 b fi(o) 382 636 y fk(!)482 642 y fi(o)538 636 y fk(!)639 642 y fi(o)104 746 y(por)31 b fg(tt)36 b fk(?)24 b fl(=)g fg(tt)104 850 y fi(por)31 b fk(?)d fg(tt)k fl(=) 24 b fg(tt)104 953 y fi(por)31 b fg(\013)47 b(\013)41 b fl(=)24 b fg(\013)40 1099 y fk(\017)d fl(P)n(arallel)30 b(conditional)q(s:)104 1202 y fg(pif)201 1222 y ff(\033)268 1202 y fl(:)43 b fi(o)391 1196 y fk(!)491 1202 y fi(\033) 558 1196 y fk(!)658 1202 y fi(\033)725 1196 y fk(!)825 1202 y fi(\033)104 1306 y fg(pif)201 1326 y ff(\033)268 1306 y fk(?)28 b fi(x)h(x)24 b fl(=)g fi(x)p fl(,)104 1410 y fg(pif)201 1430 y ff(\033)268 1410 y fg(tt)36 b fi(x)29 b fk (?)24 b fl(=)f fi(x)p fl(,)104 1514 y fg(pif)201 1533 y ff(\033)268 1514 y fg (\013)46 b fk(?)29 b fi(x)24 b fl(=)g fi(x)p fl(,)86 b(for)29 b fi(\033)e fl (=)d fi(\023;)15 b(o)40 1659 y fk(\017)21 b fl(It)29 b(is)h(w)n(ell)g(kno)n (wn)f(that)g fi(por)s fl(,)f fg(pif)1193 1679 y ff(o)1224 1659 y fl(,)h fg (pif)1374 1679 y ff(\023)1425 1659 y fl(are)104 1763 y(extensionall)q(y)j(equ\ iv)-5 b(alen)n(t)32 b([Stough)n(ton,)c(Curien])944 2748 y fh(16)p eop %%Page: 17 18 bop 25 160 a fm(In)m(tensional)42 b(equiv)-6 b(alence)0 321 y 1947 2 v 40 538 a fk(\017)21 b fj(Prop:)39 b fi(por)30 b fl(and)f fg(pif)802 558 y ff(o)861 538 y fl(are)g(in)n(tensionall)q(y)j(equiv)-5 b(alen)n(t)40 683 y fk(\017)21 b fl(Pro)r(of:)104 850 y fi(por)26 b fl(=)e fi(\025xy)t(:)k fg(pif)639 869 y ff (o)699 850 y fi(x)h fg(tt)36 b fi(y)s fl(,)104 953 y fg(pif)201 973 y ff(o) 256 953 y fl(=)23 b fi(\025bxy)t(:)29 b(por)705 966 y fh(3)765 953 y fl(\()p fi(pand)h(b)e(x)p fl(\))765 1057 y(\()p fi(pand)i fl(\()p fi(not)e(b)p fl(\)) i fi(y)s fl(\))765 1161 y(\()p fi(pand)g(x)f(y)s fl(\))40 1327 y fk(\017)21 b fl(P)n(arallel)30 b(conjunction:)208 1493 y fi(pand)24 b fl(=)g fi(\025xy)s (:)29 b(not)f fl(\()p fi(por)k fl(\()p fi(not)c(x)p fl(\))i(\()p fi(not)e(y)t fl(\)\))944 2748 y fh(17)p eop %%Page: 18 19 bop 25 160 a fm(Kno)m(wn)39 b(implemen)m(tati)q(ons)0 321 y 1947 2 v 40 538 a fk(\017)21 b fj(Prop:)38 b fg(pif)479 558 y ff(\023)529 538 y fl(can)27 b(imp\ lemen)n(t)g fg(pif)1204 558 y ff(o)1262 538 y fl(in)g(constan)n(t-depth:)104 701 y fg(pif)201 721 y ff(o)256 701 y fl(=)c fi(\025bxy)t(:)29 b fl(\(=)24 b (1)29 b(\()p fg(pif)907 721 y ff(\023)959 701 y fi(b)g fl(\()p fk(\033)1125 714 y ff(\023)1172 701 y fi(x)g fl(1)g(0\))g(\()p fk(\033)1527 714 y ff(\023) 1575 701 y fi(y)j fl(1)c(0\)\)\))40 964 y fk(\017)21 b fl(W)-7 b(ell)31 b(kno) n(wn)e(implemen)n(tation)g(of)g fg(pif)1382 984 y ff(\023)1434 964 y fl(using) g fi(por)r fl(:)104 1130 y fg(pif)201 1150 y ff(\023)248 1130 y fl(=)24 b fi (Y)19 b(F)26 b fl(0)p fi(;)43 b fl(where)104 1234 y fi(F)36 b fl(=)24 b fi (\025f)10 b(nbxy)s(:)52 b fk(\033)714 1247 y ff(\023)766 1234 y fl(\()p fi (por)32 b fl(\()p fi(pand)d fl(\(=)24 b fi(x)29 b(n)p fl(\))g(\(=)c fi(y)32 b (n)p fl(\)\))955 1338 y(\()p fi(pand)d(b)g fl(\(=)24 b fi(x)29 b(n)p fl(\)\)) 955 1442 y(\()p fi(pand)g fl(\()p fi(not)g(b)p fl(\))g(\(=)24 b fi(y)32 b(n)p fl(\)\)\))766 1546 y fi(n)766 1649 y fl(\()p fi(f)39 b fl(\(+1)29 b fi(n)p fl (\))g fi(b)f(x)h(y)t fl(\))40 1934 y fk(\017)21 b fl(This)29 b(is)h(not)f(con\ stan)n(t-depth)944 2748 y fh(18)p eop %%Page: 19 20 bop 25 160 a fm(In)m(tensional)42 b(separation)0 321 y 1947 2 v 40 538 a fk (\017)21 b fj(Lemma)32 b(1:)39 b fl(It)29 b(is)h(not)f(p)r(ossible)i(to)e(wri\ te)h(a)f(program)104 642 y(in)g(PCF)g(+)g fi(por)r fl(,)f(whic)n(h)i(computes) e fg(pif)1411 662 y ff(\023)1463 642 y fi(b)g(x)h(y)j fl(and)d(is)104 746 y (of)g(the)g(form)f fk(\033)621 759 y ff(\023)668 746 y fi(B)33 b(x)c(y)s fl (,)g(where)g fi(B)k fl(is)d(a)e(static)j(circuit)104 850 y(yielding)h(a)c(b)s (o)r(olean)40 995 y fk(\017)21 b fj(Lemma)32 b(2:)39 b fl(It)29 b(is)h(not)f (p)r(ossible)i(to)e(write)h(a)f(program)104 1099 y(in)g(PCF)g(+)g fi(por)r fl (,)f(whic)n(h)i(computes)e fg(pif)1411 1118 y ff(\023)1463 1099 y fi(b)g(x)h (y)j fl(and)d(is)104 1202 y(of)g(the)g(form)f fk(\033)621 1215 y ff(\023)668 1202 y fi(B)33 b(N)835 1215 y fh(1)896 1202 y fi(N)965 1215 y fh(2)997 1202 y fl(,)c(where)g fi(B)t fl(,)g fi(N)1490 1215 y fh(1)1522 1202 y fl(,)g fi(N) 1644 1215 y fh(2)1704 1202 y fl(are)104 1306 y(static)i(circuits)g(yielding)h (a)c(b)r(o)s(olean)i(and)e(t)n(w)n(o)104 1410 y(in)n(tegers)i(resp)r(ectiv)n (ely)40 1555 y fk(\017)21 b fj(Prop:)39 b fl(PCF)28 b(+)h fi(por)i fl(cannot) e(implemen)n(t)f fg(pif)1641 1575 y ff(\023)1693 1555 y fl(with)i(a)104 1659 y (constan)n(t-depth)f(circuit)944 2748 y fh(19)p eop %%Page: 20 21 bop 25 160 a fm(Query)40 b(is)g(more)g(p)t(o)m(w)m(erful)0 321 y 1947 2 v 40 538 a fk(\017)21 b fl(Assume)26 b(existence)k(of)e(binary)g(addition)h(op)r (eration)g(in)104 642 y(PCF)40 787 y fk(\017)21 b fj(Prop:)39 b fl(PCF)28 b (+)h fg(pif)781 807 y ff(\023)833 787 y fl(cannot)g(implemen)n(t)f fi(n)p fl (-ary)104 891 y(addition)i(in)g(depth)f fi(l)r(og)i(n)40 1036 y fk(\017)21 b fj(Corollary:)41 b fl(PCF)29 b(+)f fi(por)j fl(cannot)e(implemen)n(t)g fi(n)p fl(-ary)104 1140 y(addition)h(in)g(depth)f fi(l)r(og)i(n)40 1285 y fk(\017)21 b fl(Hierarc)n(h)n(y)28 b(of)i(in)n(tensional)h(expressiv)n(eness)f(for)104 1389 y(deterministic)h(parallel)g(constructs:)906 1541 y 239 2 v 79 x 2 79 v 920 1591 a(query)1143 1620 y 2 79 v 906 1622 a 239 2 v 951 1707 a 149 2 v 105 x 2 105 v 965 1779 a fg(pif)1062 1799 y ff(\023)1098 1812 y 2 105 v 951 1814 a 149 2 v 826 1922 a 155 2 v 78 x 2 79 v 840 1971 a fi(por)979 2000 y 2 79 v 826 2002 a 155 2 v 1040 1899 a 157 2 v 104 x 2 105 v 1054 1971 a fg(pif)1151 1991 y ff(o)1194 2003 y 2 105 v 1040 2005 a 157 2 v 40 2173 a fk(\017)21 b fl(W)-7 b(e)29 b(ha)n(v)n(e)g(exhibited)i(languages)f(extensionall)q(y)i(but)104 2276 y(not)d(in)n(tensionally)k(equiv)-5 b(alen)n(t)944 2748 y fh(20)p eop %%Page: 21 22 bop 25 170 a fm(Recursion-free)42 b(PCF)0 321 y 1947 2 v 40 538 a fk(\017)21 b fl(A)28 b(sligh)n(tly)k(mo)q(di\014ed)d(PCF)40 683 y fk(\017)21 b fl(T)n (yp)r(es:)208 829 y fi(\033)32 b fl(:)14 b(:)g(=)24 b fi(o)k fk(j)h fi(\023)g fk(j)g fi(\033)757 823 y fk(!)858 829 y fi(\033)40 995 y fk(\017)21 b fl(Syn) n(tax:)208 1140 y fi(M)37 b fl(:)14 b(:)h(=)24 b fi(c)29 b fk(j)f fi(x)h fk (j)g fi(\025x:)g(M)37 b fk(j)29 b fi(M)9 b(M)40 1306 y fk(\017)21 b fl(Consta\ n)n(ts:)228 1445 y fg(tt)8 b fi(;)14 b fg(\013)47 b fl(:)c fi(o)228 1549 y (n)29 b fl(:)43 b fi(\023)228 1653 y fl(=)p fi(;)15 b(<;)f(>;)g fk(\024)p fi (;)g fk(\025)29 b fl(:)43 b fi(\023)857 1647 y fk(!)957 1653 y fi(\023)1002 1647 y fk(!)1102 1653 y fi(o)228 1757 y fl(+)p fi(;)15 b fk(\000)28 b fl(:)43 b fi(\023)541 1751 y fk(!)641 1757 y fi(\023)686 1751 y fk(!)787 1757 y fi (\023)228 1860 y fk(\033)295 1873 y ff(\033)362 1860 y fl(:)g fi(o)485 1854 y fk(!)586 1860 y fi(\033)652 1854 y fk(!)753 1860 y fi(\033)820 1854 y fk(!) 920 1860 y fi(\033)217 b fl(\(conditional,)32 b fi(\033)27 b fk(2)d(f)p fi (o;)14 b(\023)p fk(g)p fl(\))228 1964 y(\012)290 1933 y ff(\033)358 1964 y fl (:)43 b fi(\033)712 b fl(\(unde\014ned)28 b(elemen)n(ts\))40 2121 y fk(\017) 21 b fl(Standard)28 b(denotational)k(seman)n(tics)c(for)h(PCF:)104 2225 y fk (D)s fl(:)14 b(T)-7 b(erms)458 2219 y fk(!)558 2225 y fl(En)n(vironmen)n(ts) 1094 2219 y fk(!)1194 2225 y([)p fi(D)1322 2238 y ff(\033)944 2748 y fh(21)p eop %%Page: 22 23 bop 25 160 a fm(Deterministi)q(c)42 b(query)0 321 y 1947 2 v 40 537 a fk(\ \017)21 b fl(Syn)n(tax:)104 641 y(query)29 b(:)43 b(\()p fi(\033)492 654 y fh (1)544 641 y fk(\002)19 b(\001)14 b(\001)h(\001)k(\002)g fi(\033)885 654 y ff (n)923 641 y fl(\))971 635 y fk(!)1071 641 y fi(\034)104 745 y fl(query)29 b (\()p fi(x)425 704 y ff(\033)459 715 y fd(1)425 760 y fh(1)489 745 y fi(;)14 b (:)g(:)g(:)h(;)f(x)729 714 y ff(\033)763 723 y fc(n)729 766 y ff(n)796 745 y fl(\))30 b(is)222 849 y fi(p)265 861 y fh(1)321 849 y fk(\))24 b fi(M)524 817 y ff(\034)515 870 y fh(1)222 952 y fi(:)14 b(:)g(:)222 1056 y(p)265 1069 y ff (k)324 1056 y fk(\))24 b fi(M)527 1025 y ff(\034)518 1077 y(k)40 1201 y fk (\017)d fl(Consisten)n(t)30 b(inputs)g(pro)r(duce)e(same)g(output:)222 1305 y (if)i fi(p)344 1318 y ff(i)391 1305 y fk(*)23 b fi(p)510 1318 y ff(j)569 1305 y fl(then)29 b fk(D)s fl([)-14 b([)p fi(M)952 1318 y ff(i)974 1305 y fl(])g (])23 b(=)h fk(D)s fl([)-14 b([)p fi(M)1309 1318 y ff(j)1338 1305 y fl(])g (].)40 1450 y fk(\017)21 b fl(DPCF)28 b(=)h(PCF)g(+)f(deterministic)j(query) 944 2748 y fh(22)p eop %%Page: 23 24 bop 25 160 a fm(Deterministi)q(c)42 b(query:)53 b(Seman)m(tics)0 321 y 1947 2 v -112 536 a fk(D)-46 549 y ff(pat)69 536 y fl(:)43 b(P)n(atterns)470 530 y fk (!)570 536 y fl(En)n(vironmen)n(ts)1106 530 y fk(!)1192 536 y fl(\()p fi(D) 1296 549 y fc(B)s(ool)1420 536 y fk(\002)19 b fl(En)n(vironmen)n(ts)o(\))-112 743 y fk(D)s fl([)-14 b([)p fi(Q)p fl(])f(])p fi(\032)24 b fl(=)f(am)n(b)412 756 y ff(k)447 743 y fl(\()p fk(D)s fl([)-14 b([)o fi(~)-42 b(x)28 b fl(is)i fi(p)790 756 y fh(1)846 743 y fk(\))24 b fi(M)1049 712 y ff(\034)1040 765 y fh (1)1084 743 y fl(])-14 b(])p fi(\032;)13 b(:)i(:)f(:)g(;)g 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fd(1)156 1278 y fh(1)219 1262 y fi(;)14 b(:)g(:)h(:)f(;)g(x)459 1231 y ff(\033)493 1240 y fc (n)459 1284 y ff(n)527 1262 y fl(\))29 b(is)h(\()p fi(e)749 1221 y ff(\033) 783 1233 y fd(1)749 1278 y fh(1)812 1262 y fi(;)14 b(:)g(:)h(:)f(;)g(e)1043 1231 y ff(\033)1077 1240 y fc(n)1043 1284 y ff(n)1111 1262 y fl(\)])-14 b(])p fi(\032)23 b fl(=)6 1366 y(\()p fi(b)76 1379 y fh(1)128 1366 y fk(^)c(\001)c (\001)f(\001)19 b(^)h fi(b)438 1379 y ff(n)475 1366 y fi(;)15 b(\026)566 1379 y fh(1)622 1366 y fk(j)23 b(\001)15 b(\001)f(\001)24 b(j)g fi(\026)894 1379 y ff(n)931 1366 y fl(\))p fi(;)15 b fl(where)29 b(\()p fi(b)1322 1379 y ff(i) 1345 1366 y fi(;)14 b(\026)1435 1379 y ff(i)1458 1366 y fl(\))24 b(=)g fk(D) 1672 1379 y ff(pat)1758 1366 y fl([)-14 b([)p fi(x)1841 1324 y ff(\033)1875 1336 y fc(i)1841 1383 y ff(i)1924 1366 y fl(is)30 b fi(e)2051 1324 y ff(\033) 2085 1336 y fc(i)2051 1383 y ff(i)2106 1366 y fl(])-15 b(])p fi(\032)-112 1678 y fk(D)-46 1691 y ff(pat)40 1678 y fl([)h([)p fi(x)123 1647 y ff(\033)190 1678 y fl(is)29 b fi(e)316 1647 y ff(\033)355 1678 y fl(])-15 b(])p fi(\032)24 b fl (=)548 1507 y fb(8)548 1545 y(>)548 1557 y(>)548 1570 y(>)548 1582 y(>)548 1594 y(>)548 1607 y(>)548 1619 y(<)548 1694 y(>)548 1707 y(>)548 1719 y(>)548 1731 y(>)548 1744 y(>)548 1756 y(>)548 1769 y(:)605 1574 y fl(\()p fk(D)t fl ([)-15 b([)p fi(x)790 1542 y ff(\033)829 1574 y fl(])g(])p fi(\032)24 b fl (=)f fk(D)s fl([)-14 b([)p fi(e)1164 1542 y ff(\033)1202 1574 y fl(])g(])p fi (\032;)13 b fk(?)p fl(\))p fi(;)42 b fl(if)30 b fi(e)1603 1542 y ff(\033)1670 1574 y fl(is)g(closed)605 1677 y(\()p fg(tt)8 b fi(;)14 b(y)788 1646 y ff(\ \033)850 1677 y fk(7!)24 b fi(x)1009 1646 y ff(\033)1048 1677 y fl(\))p fi (;)379 b fl(if)30 b fi(e)1603 1646 y ff(\033)1666 1677 y fk(\021)23 b fi(y) 1802 1646 y ff(\033)605 1781 y fl(\()p fg(tt)8 b fi(;)14 b fk(?)p fl(\))p fi (;)618 b fl(if)30 b fi(e)1603 1750 y ff(\033)1666 1781 y fk(\021)1756 1788 y 58 2 v -118 2033 a fl(McCarth)n(y's)f(am)n(biguit)n(y)g(op)r(erator:)-118 2137 y fi(amb)p fl(\()p fk(?)p fi(;)15 b(x)p fl(\))24 b(=)g fi(x)p fl(,)-118 2241 y fi(amb)p fl(\()p fi(x;)15 b fk(?)p fl(\))24 b(=)g fi(x)p fl(,)-118 2345 y fi (amb)p fl(\()p fi(x;)15 b(y)s fl(\))25 b(=)e fi(x)29 b fj(or)g fi(y)t(:)944 2748 y fh(23)p eop %%Page: 24 25 bop 25 160 a fm(Nondeterministi)q(c)43 b(query)0 321 y 1947 2 v 40 538 a fk (\017)21 b fl(Example:)104 642 y fi(not)229 655 y fe(?)301 642 y fk(\021)j fi (\025x:)29 b fl(query)g(\()p fi(x)p fl(\))h(is)540 746 y fg(tt)h fk(\))24 b fg (\013)482 850 y fk(j)k fg(\013)42 b fk(\))24 b fg(\013)482 953 y fk(j)534 960 y 58 2 v 616 953 a(\))g fg(tt)40 1099 y fk(\017)d fl(Under)28 b(the)h(seman)n (tics)g(of)g(deterministic)i(query)-7 b(,)104 1202 y(nondeterministic)31 b (query)e(is)h(not)f(in)n(tensionally)j(more)104 1306 y(expressiv)n(e.)944 2748 y fh(24)p eop %%Page: 25 26 bop 25 160 a fm(Nondeterministi)q(c)43 b(query:)52 b(Seman)m(tics)0 321 y 1947 2 v 40 537 a fk(\017)21 b fl(Seman)n(tics:)110 845 y fk(D)176 858 y ff (pat)262 845 y fl([)-14 b([)p fi(x)345 814 y ff(\033)412 845 y fl(is)498 852 y 58 2 v 556 858 a ff(ij)606 845 y fl(])g(])p fi(\032)23 b fl(=)799 624 y fb (8)799 662 y(>)799 674 y(>)799 687 y(>)799 699 y(>)799 712 y(>)799 724 y(>) 799 736 y(>)799 749 y(>)799 761 y(>)799 774 y(>)799 786 y(<)799 861 y(>)799 873 y(>)799 886 y(>)799 898 y(>)799 911 y(>)799 923 y(>)799 936 y(>)799 948 y (>)799 961 y(>)799 973 y(>)799 986 y(:)857 689 y fl(\(not)15 b(\(p)s(oll)30 b fi(x)1281 658 y ff(\033)1320 689 y fl(\))p fi(;)15 b fk(?)p fl(\))p fi(;)975 793 y fl(if)30 b(exhausted)q(\()p fi(x)1512 761 y ff(\033)1551 793 y fi(;)14 b (i;)g(j;)h(p)1774 805 y fh(1)1806 793 y fi(;)f(:)h(:)f(:)g(;)h(p)2041 805 y ff (k)2076 793 y fi(;)f(\032)p fl(\))857 896 y(\()p fg(tt)8 b fi(;)14 b fk(?)p fl (\))p fi(;)975 1000 y fl(otherwise)110 1157 y(exhausted)q(\()p fi(x)568 1125 y ff(o)600 1157 y fi(;)g(i;)g(j;)h(p)823 1169 y fh(1)855 1157 y fi(;)f(:)h(:)f (:)g(;)h(p)1090 1169 y ff(k)1125 1157 y fi(;)f(\032)p fl(\))24 b(=)1356 1035 y fb(8)1356 1073 y(>)1356 1085 y(>)1356 1098 y(<)1356 1172 y(>)1356 1185 y(>) 1356 1197 y(:)1414 1104 y fg(tt)7 b fi(;)47 b fl(if)30 b(Prop)1812 1124 y ff (o)1414 1208 y fg(\013)18 b fi(;)41 b fl(otherwise)110 1364 y(exhausted)q(\() p fi(x)568 1333 y ff(\023)592 1364 y fi(;)14 b(i;)g(j;)h(p)815 1377 y fh(1) 847 1364 y fi(;)g(:)f(:)g(:)g(;)h(p)1082 1377 y ff(k)1117 1364 y fi(;)f(\032) p fl(\))24 b(=)1348 1243 y fb(8)1348 1280 y(>)1348 1293 y(>)1348 1305 y(<) 1348 1380 y(>)1348 1392 y(>)1348 1405 y(:)1406 1311 y fg(tt)7 b fi(;)47 b fl (if)30 b(Prop)1804 1331 y ff(\023)1406 1415 y fg(\013)18 b fi(;)41 b fl(other\ wise)40 1584 y fk(\017)21 b fl(Prop)287 1604 y ff(o)342 1584 y fk(\021)125 1681 y fl(\(\()p fk(9)p fi(l)r(;)14 b(m:)28 b fk(D)s fl([)-14 b([)p fi(e)576 1693 y ff(l)q(j)625 1681 y fl(])f(])p fi(\032)24 b fl(=)f fg(tt)k fk(^)19 b (D)s fl([)-14 b([)p fi(e)1121 1693 y ff(mj)1203 1681 y fl(])g(])p fi(\032)23 b fl(=)h fg(\013)18 b fl(\))29 b fk(_)153 1784 y fl(\()p fk(9)p fi(l)r(:)g fk (D)r fl([)-14 b([)p fi(e)457 1797 y ff(l)q(j)506 1784 y fl(])g(])p fi(\032)23 b fl(=)h fi(y)744 1753 y ff(o)775 1784 y fl(\)\))c fk(^)g fl(\()p fi(p)1014 1797 y fh(1)1047 1784 y fk(n)p fi(j)29 b fk(*)23 b(\001)15 b(\001)f(\001)24 b (*)f fi(p)1474 1797 y ff(k)1510 1784 y fk(n)p fi(j)5 b fl(\))40 1926 y fk(\ \017)21 b fl(Prop)287 1945 y ff(\023)334 1926 y fk(\021)j fl(\()p fk(9)p fi (l)r(:)k fk(D)s fl([)-14 b([)p fi(e)729 1939 y ff(l)q(j)778 1926 y fl(])f(])p fi(\032)24 b fl(=)g fi(y)1016 1894 y ff(\023)1039 1926 y fl(\))c fk(^)f fl (\()p fi(p)1244 1939 y fh(1)1277 1926 y fk(n)p fi(j)29 b fk(*)24 b(\001)14 b (\001)g(\001)24 b(*)g fi(p)1705 1939 y ff(k)1740 1926 y fk(n)p fi(j)6 b fl (\))40 2071 y fk(\017)21 b fl(NPCF)28 b(=)h(PCF)f(+)h(nondeterministic)i(quer\ y)944 2748 y fh(25)p eop %%Page: 26 27 bop 25 160 a fm(Circuit)41 b(seman)m(tics:)53 b(Buildi)q(ng)43 b(blo)t(c)m (ks)0 321 y 1947 2 v 147 6861 a @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: ../drawings/buildblocks1.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.62069 0 0 0.62069 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict [ 1 0 0 1 -2 418 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -19 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 129.5 777 ] concat [ (n) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 92 776 ] concat [ (tt) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 19 279 ] concat 105 485 123 502 Rect End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 57 279 ] concat 105 485 123 502 Rect End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -19 279 ] concat 114 485 114 472 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 20 279 ] concat 114 485 114 472 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 57 279 ] concat 114 485 114 472 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -19 280 ] concat 114 451 114 416 Line End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 100 731 ] concat [ (x) ] Text End Begin %I Pict Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -19 279 ] concat 140 451 166 451 153 425 140 451 4 Poly End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 132.5 724 ] concat [ (f) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -2 392 ] concat 136 312 136 304 Line End End %I eop Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 56.5 777 ] concat [ (\(a\)) ] Text End Begin %I Text 0 0 0 SetCFg /Times-Roman 12 SetF [ 1 0 0 1 56.5 716 ] concat [ (\(b\)) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 200 716 ] concat [ (\(c\)) ] Text End Begin %I Pict [ 1 0 0 1 0 1.50009 ] concat Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 53.5 560 ] concat 353 340 353 270 Line End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 81.5 576.5 ] concat 293 236 301 244 Rect End End %I eop Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 168 777 ] concat [ (=) ] Text End Begin %I Pict Begin %I Pict [ 1 0 0 1 140.5 181 ] concat Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -5 475 ] concat 218 240 234 240 244 232 234 224 218 224 5 BSpl End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 118 162 162 196 Rect End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 385 437 359 463 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 385 437 385 463 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 385 437 411 463 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 385 403 385 377 Line End End %I eop Begin %I Pict [ 1 0 0 1 19.5 0 ] concat Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 187 437 169 463 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 187 437 205 463 Line End End %I eop Begin %I Pict Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 206.5 776.5 ] concat [ (+) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 96 279 ] concat 105 485 123 502 Rect End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 96 279 ] concat 114 485 114 472 Line End Begin %I Pict [ 1 0 0 1 58.5 0 ] concat Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 187 437 169 463 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 57.5 562.5 ] concat 187 437 205 463 Line End End %I eop End %I eop End %I eop End %I eop showpage end %%EndDocument @endspecial 102 1286 a fl(\(a\))29 b(constan)n(ts,)h(\(b\))f(v)-5 b(ariables\ ,)31 b(\(c\))f(ignored)f(inputs)-33 7665 y @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: ../drawings/buildblocks2.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.62069 0 0 0.62069 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict [ 1 0 0 1 -230 402 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 296 716 ] concat [ (\(d\)) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 367 716 ] concat [ (\(e\)) ] Text End Begin %I Pict [ 1 0 0 1 -1 0 ] concat Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 248 343 ] concat 140 451 166 451 153 425 140 451 4 Poly End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 396.5 790 ] concat [ (N) ] Text End End %I eop Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 141 403 ] concat 241 352 276 352 259 318 241 352 4 Poly End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 395 747 ] concat [ (M) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 141 403 ] concat 259 365 250 352 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 141 403 ] concat 259 365 267 352 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 141 403 ] concat 259 318 259 309 Line End Begin %I Pict [ 1 0 0 1 0 -9 ] concat Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 69 412 ] concat 241 352 276 352 259 318 241 352 4 Poly End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 323 756 ] concat [ (M) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 336 790 ] concat [ (x) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 69 412 ] concat 259 365 250 352 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 69 412 ] concat 259 365 267 352 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 69 412 ] concat 259 318 259 309 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -4 265 ] concat 332 512 332 525 Line End End %I eop Begin %I Pict /Helvetica 12 SetF [ 1 0 0 1 270 -55 ] concat Begin %I Pict [ 1 0 0 1 9 -1 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 245 777.5 ] concat [ (poll) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 192.5 551.5 ] concat 95 425 155 461 Rect End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 55.5 552 ] concat 415 458 415 484 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 55.5 552 ] concat 415 421 415 398 Line End End %I eop Begin %I Pict [ 1 0 0 1 395 0 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 114 485 114 472 Line End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End Begin %I Pict [ 1 0 0 1 -1.5 0 ] concat Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 74 440 56 466 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 74 440 92 466 Line End End %I eop End %I eop Begin %I Pict /Helvetica 12 SetF [ 1 0 0 1 312 -55 ] concat Begin %I Pict [ 1 0 0 1 1.99998 0 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 204 406 264 440 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 164 777 ] concat [ (amb) ] Text End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 238 406 238 380 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 238 440 212 466 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 238 440 264 466 Line End End %I eop Begin %I Pict [ 1 0 0 1 356 0 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 60 561 ] concat 204 406 264 440 Rect End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 238 406 238 380 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 238 440 212 466 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 238 440 264 466 Line End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 166.5 777 ] concat [ (and) ] Text End End %I eop Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 449 751 ] concat [ (\(f\)) ] Text End End %I eop End %I eop showpage end %%EndDocument @endspecial 194 2187 a(\(d\))g(abstraction,)h(\(e\))g(applicatio)q(n,)h(\(f) 7 b(\))30 b(query)944 2748 y fh(26)p eop %%Page: 27 28 bop 25 160 a fm(Circuit)41 b(seman)m(tics:)53 b(PCF)40 b(examples)0 321 y 1947 2 v 9 6936 a @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: ../drawings/pcfexamples.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.923077 0 0 0.923077 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 23.5 560 ] concat 177 468 177 356 Line End Begin %I Pict [ 1 0 0 1 30 0 ] concat Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 560 ] concat 195 468 195 408 Line End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 -4.5 599 ] concat 195 322 203 330 Rect End End %I eop Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 115 794.5 ] concat [ (x) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 128 794.5 ] concat [ (y) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 39 716 ] concat [ (\(a\)) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 113 716 ] concat [ (\(b\)) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 191 716 ] concat [ (\(c\)) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 23.5 599 ] concat 31 382 65 416 Rect End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 23.5 560 ] concat 31 382 65 416 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 44 763.5 ] concat [ (+) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 45 802.5 ] concat [ (2) ] Text End Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 560 ] concat 99 460 83 434 99 416 3 BSpl End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 560 ] concat 99 382 99 356 Line End Begin %I MLine 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 19.5 551 ] concat 341 442 377 442 359 400 341 442 4 MLine End Begin %I MLine 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 19.5 587 ] concat 341 442 377 442 359 400 341 442 4 MLine End Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 560 ] concat 99 460 117 434 99 416 3 BSpl End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 198 768.5 ] concat [ (f) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 198 804.5 ] concat [ (f) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 201.5 821.5 ] concat [ (x) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 560 ] concat 403 382 403 356 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 561 ] concat 403 520 403 494 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 -2.5 560 ] concat 403 454 403 425 Line End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 1.5 555 ] concat 203 392 265 434 Rect End End %I eop showpage end %%EndDocument @endspecial 145 1703 a fl(\(a\))30 b(\()p fi(\025x:)g(x)19 b fl(+)g fi(x)p fl (\)2,)29 b(\(b\))h fi(\025xy)t(:)e(x)p fl(,)h(\(c\))h fi(\025f)10 b(x:)28 b (f)10 b fl(\()p fi(f)g(x)p fl(\))944 2748 y fh(27)p eop %%Page: 28 29 bop 25 160 a fm(Circuit)41 b(seman)m(tics:)53 b(Query)40 b(examples)0 321 y 1947 2 v -255 4604 a @beginspecial 1.300000 @hscale 1.300000 @vscale @setspecial %%BeginDocument: ../drawings/bothexamples.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.923077 0 0 0.923077 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict [ 1 0 0 1 -69 43 ] concat Begin %I Pict [ 1 0 0 1 106.5 -146.5 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 39 26 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 108 635 ] concat [ (tt) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 128 240 162 274 Rect End End %I eop Begin %I Pict [ 1 0 0 1 100 26 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 108 635 ] concat [ (tt) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 128 240 162 274 Rect End End %I eop Begin %I Pict [ 1 0 0 1 168.5 78 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 117 583 ] concat [ (ff) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 144 136 180 170 Rect End End %I eop Begin %I Pict [ 1 0 0 1 9 -18 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 173 773 ] concat [ (x) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 207 774 ] concat [ (y) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 45 503 ] concat 246 496 246 540 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 45 503 ] concat 316 496 316 540 Line End End %I eop Begin %I Pict [ 1 0 0 1 167 -146.5 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 45 -146.5 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 121 -39 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 112 730 ] concat [ (not) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 70 346 122 380 Rect End End %I eop Begin %I Pict [ 1 0 0 1 156 -39 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 112 730 ] concat [ (not) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 70 346 122 380 Rect End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 372 208 372 182 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 373 182 432 208 Line End Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 278 380 226 234 252 182 3 BSpl End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 130 182 156 208 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 252 182 278 208 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 130 146 252 94 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 252 94 252 146 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 252 94 372 146 Line End Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 208 380 96 234 130 182 3 BSpl End Begin %I Pict [ 1 0 0 1 -38 25.5 ] concat Begin %I Pict [ 1 0 0 1 62 -216 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 204 406 264 440 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 164 777 ] concat [ (amb) ] Text End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 118 345 ] concat 238 406 238 380 Line End End %I eop Begin %I Pict [ 1 0 0 1 -82 30.9999 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 224 414 ] concat 204 406 264 440 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 330.5 630 ] concat [ (and) ] Text End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 145 559 ] concat 64 350 194 272 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 145 559 ] concat 134 350 262 272 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 145 559 ] concat 194 238 228 212 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 145 559 ] concat 228 212 266 238 Line End End %I eop Begin %I Pict /Helvetica 12 SetF [ 1 0 0 1 30 246 ] concat Begin %I Pict [ 1 0 0 1 227.5 -349.5 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 291.5 -177 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 108 635 ] concat [ (tt) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 128 240 162 274 Rect End End %I eop Begin %I Pict [ 1 0 0 1 151 -125 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 117 583 ] concat [ (ff) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 144 136 180 170 Rect End End %I eop Begin %I Pict [ 1 0 0 1 143 -202 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 182 755 ] concat [ (x) ] Text End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 54 485 ] concat 246 496 246 540 Line End End %I eop Begin %I Pict [ 1 0 0 1 288 -349.5 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 166 -349.5 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -21 279 ] concat 105 485 123 502 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 90 777 ] concat [ (if) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 189 -272 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 112 730 ] concat [ (not) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 70 346 122 380 Rect End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 194 341 ] concat 130 182 156 208 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 194 341 ] concat 130 146 252 94 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 194 341 ] concat 252 94 252 146 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 194 341 ] concat 252 94 372 146 Line End Begin %I Pict [ 1 0 0 1 216.5 -125 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 117 583 ] concat [ (ff) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 40 502 ] concat 144 136 180 170 Rect End End %I eop Begin %I Pict [ 1 0 0 1 119.5 -173 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 245.5 661.5 ] concat [ (poll) ] Text End Begin %I Poly 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 192.5 435.5 ] concat 95 425 95 459 155 459 155 425 4 Poly End End %I eop Begin %I BSpl 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 230 481 56 351 108 283 3 BSpl End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 230 481 212 343 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 230 481 337 404 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 212 309 230 283 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 230 283 264 309 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 342 309 350 283 Line End Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 205 290.5 ] concat 350 282 398 309 Line End Begin %I Pict [ 1 0 0 1 83 -177.5 ] concat Begin %I Pict [ 1 0 0 1 62 -216 ] concat Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 58 561 ] concat 204 406 264 440 Rect End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 164 777 ] concat [ (amb) ] Text End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 118 345 ] concat 238 406 238 380 Line End End %I eop Begin %I Pict [ 1 0 0 1 254 -272 ] concat Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 112 730 ] concat [ (not) ] Text End Begin %I Rect 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 73 544 ] concat 70 346 122 380 Rect End End %I eop Begin %I Line 1 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0 SetP [ 0.5 0 0 0.5 216 289 ] concat 318 372 318 346 Line End End %I eop Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 122 587 ] concat [ (\(a\)) ] Text End Begin %I Text 0 0 0 SetCFg /Helvetica 12 SetF [ 1 0 0 1 342 587 ] concat [ (\(b\)) ] Text End End %I eop showpage end %%EndDocument @endspecial 656 2012 a fl(\(a\))30 b fi(por)r fl(,)f(\(b\))g fi(not)1242 2025 y fe(?)944 2748 y fh(28)p eop %%Page: 29 30 bop 25 160 a fm(Circuit)41 b(seman)m(tics:)53 b(Prop)t(erties)42 b(I)0 321 y 1947 2 v 40 538 a fk(\017)21 b fl(De\014ne)28 b(extended)i(seman)n(tics)f(for) g(PCF:)104 642 y fk(E)8 b fl(:)14 b(T)-7 b(erms)442 636 y fk(!)543 642 y fl (En)n(vironmen)n(ts)1078 636 y fk(!)1164 642 y fl(\()p fk([)p fi(D)1325 655 y ff(\033)1384 642 y fk(\002)19 b fl(S-T)-7 b(erms)1779 606 y fh(2)1811 642 y fl (\))104 826 y fg(depth)6 b fl(\()p fi(M)428 838 y fh(1)460 826 y fl(+)q fi (M)612 838 y fh(2)643 826 y fl(\))25 b(=)f(1)q(+)q(max)n(\()p fg(depth)6 b fl (\()p fi(M)1420 838 y fh(1)1452 826 y fl(\))p fi(;)15 b fg(depth)6 b fl(\()p fi(M)1848 838 y fh(2)1880 826 y fl(\)\))104 950 y fg(depth)g fl(\()p fi(x)393 919 y ff(\033)432 950 y fl(\))24 b(=)g fi(x)629 919 y ff(\033)104 1075 y fg (depth)6 b fl(\()p fi(M)428 1088 y fh(1)488 1075 y fi(M)572 1088 y fh(2)604 1075 y fl(\))24 b(=)g fg(depth)6 b fl(\()p fi(M)1076 1088 y fh(1)1108 1075 y fl(\))29 b fg(depth)6 b fl(\()p fi(M)1494 1088 y fh(2)1526 1075 y fl(\))104 1199 y fg(depth)g fl(\()p fi(\025x)443 1168 y ff(\033)482 1199 y fi(:)28 b (M)9 b fl(\))25 b(=)f(\003)p fi(x)885 1168 y ff(\033)923 1199 y fi(:)29 b fg (depth)5 b fl(\()p fi(M)10 b fl(\))40 1404 y fk(\017)21 b fl(F)-7 b(or)28 b (a)h(PCF)g(program)e fi(M)8 b fl(,)29 b fk(E)8 b fl([)-14 b([)p fi(M)9 b fl (])-15 b(])p fk(?)24 b fl(=)g(\()p fi(v)s(;)14 b(d;)g(s)p fl(\))30 b(if)g(and) 104 1507 y(only)g(if)g(the)f(circuit)i(represen)n(ting)e fi(M)38 b fl(has)29 b (depth)f fi(d)104 1611 y fl(and)g(size)i fi(s)p fl(.)944 2748 y fh(29)p eop %%Page: 30 31 bop 25 160 a fm(Circuit)41 b(seman)m(tics:)53 b(Prop)t(erties)42 b(I)s(I)0 321 y 1947 2 v 40 543 a fk(\017)21 b fl([Blello)5 b(c)n(h)29 b(&)f(Greiner])h (De\014ne)g(call-b)n(y-sp)s(eculation:)104 651 y fi(\032;)14 b(d)42 b fk(`)h fi(M)33 b fk(\000)-14 b(!)626 664 y fa(cbs)701 651 y fi(v)s fl(;)14 b fi(d) 829 620 y fe(0)847 651 y fi(;)896 628 y fl(^)885 651 y fi(d)930 626 y fe(0) 949 651 y fi(;)g(w)574 834 y(\032;)g(d)43 b fk(`)f fi(M)924 847 y fh(1)980 834 y fk(\000)-15 b(!)1118 847 y fa(cbs)1193 834 y fi(v)1235 847 y fh(1)1267 834 y fl(;)14 b fi(d)1350 847 y fh(1)1382 834 y fi(;)1437 812 y fl(^)1420 834 y fi (d)1465 847 y fh(1)1497 834 y fi(;)h(w)1598 847 y fh(1)574 948 y fi(\032;)f (d)43 b fk(`)f fi(M)924 961 y fh(2)980 948 y fk(\000)-15 b(!)1118 961 y fa (cbs)1193 948 y fi(v)1235 961 y fh(2)1267 948 y fl(;)14 b fi(d)1350 961 y fh (2)1382 948 y fi(;)1437 925 y fl(^)1420 948 y fi(d)1465 961 y fh(2)1497 948 y fi(;)h(w)1598 961 y fh(2)137 986 y 1929 2 v 135 x fi(\032;)f(d)43 b fk(`)g fi (M)488 1134 y fh(1)538 1121 y fl(+)19 b fi(M)708 1134 y fh(2)764 1121 y fk (\000)-15 b(!)902 1134 y fa(cbs)999 1063 y fi(v)1041 1076 y fh(1)1091 1063 y fl(+)19 b fi(v)1219 1076 y fh(2)1251 1063 y fl(;)14 b(1)20 b(+)f(max)o(\()p fi (d)1676 1076 y fh(1)1708 1063 y fi(;)14 b(d)1791 1076 y fh(2)1823 1063 y fl (\))p fi(;)999 1177 y fl(1)19 b(+)g(max)o(\()1357 1154 y(^)1340 1177 y fi(d) 1385 1190 y fh(1)1417 1177 y fi(;)1472 1154 y fl(^)1456 1177 y fi(d)1501 1190 y fh(2)1532 1177 y fl(\))p fi(;)c fl(1)k(+)g fi(w)1814 1190 y fh(1)1865 1177 y fl(+)g fi(w)2013 1190 y fh(2)40 1417 y fk(\017)i fl(If)29 b fk(E)8 b fl([)-14 b([)p fi(M)8 b fl(])-14 b(])p fk(?)24 b fl(=)g(\()p fi(v)s(;)14 b(d;)g(s)p fl (\),)30 b(and)104 1520 y fk(?)p fi(;)14 b fl(0)43 b fk(`)g fi(M)33 b fk(\000) -15 b(!)646 1533 y fa(cbs)721 1520 y fi(v)s fl(;)15 b fi(t;)875 1505 y fl(^) 874 1520 y fi(t;)f(w)r fl(,)29 b(for)g(a)f(program)f fi(M)9 b fl(,)29 b(then:) 107 1666 y(1.)21 b fi(s)j fk(\024)g fi(w)r fl(;)107 1790 y(2.)d fi(d)j fk(\ \024)356 1774 y fl(^)355 1790 y fi(t)p fl(;)107 1915 y(3.)d(if)30 b fi(M)38 b fl(is)29 b(conditional-free)q(,)i(then)e fi(d)24 b fl(=)g fi(t)p fl(.)944 2748 y fh(30)p eop %%Page: 31 32 bop 25 170 a fm(Metho)t(d)40 b(and)f(metric)0 321 y 1947 2 v 40 538 a fk(\ \017)21 b fl(Circuit)31 b(seman)n(tics)e(de\014nes)f(parallel)k(complexit)n (y:)104 642 y(parallel)f(time)e(and)g(parallel)i(w)n(ork)40 787 y fk(\017)21 b fl(Notions)29 b(of)g(expressiv)n(eness:)125 933 y fj({)21 b fl(time-expressiv) n(eness)125 1057 y fj({)g fl(w)n(ork-expressiv)n(eness)40 1202 y fk(\017)g fl (Assume)27 b(hardw)n(are)h(that)h(can)g(detect)h(unde\014ned)104 1306 y(input\ s)40 1451 y fk(\017)21 b fl(Question:)39 b(On)29 b(suc)n(h)f(hardw)n(are,)g (is)h(NPCF)104 1555 y(in)n(tensionally)j(more)c(time-)h(or)f(w)n(ork-expressi\ v)n(e)i(than)104 1659 y(DPCF?)944 2748 y fh(31)p eop %%Page: 32 33 bop 25 170 a fm(Bo)t(olean)41 b(circuits)0 321 y 1947 2 v 40 538 a fk(\017) 21 b fl(Tw)n(o)28 b(bases)h(for)g(b)r(o)s(olean)g(circuits:)125 683 y fj({)21 b fl(monotone:)38 b(AND,)27 b(OR)125 808 y fj({)21 b fl(De)29 b(Morgan:)38 b (AND,)27 b(OR,)i(NOT)40 953 y fk(\017)21 b fl(Monotonicit)n(y:)-728 6653 y @beginspecial 2 @hscale 2 @vscale @setspecial %%BeginDocument: ../drawings/domains.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def Begin [ 0.923077 0 0 0.923077 0 0 ] concat /originalCTM matrix currentmatrix def 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