This is not my homework, I'm trying to understand LALR(1) grammars. So I found this
S -> aEa | bEb | aFb | bFa
E -> e
F -> e
I wrote the LR items, but I can't figure out why this is an LR(1) grammar and not LALR(1)?
Can anyone help me? Thank you
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1 Answer
Let's begin by constructing LR(1) configurating sets for the grammar:
(1)
S' -> .S [$]
S -> .aEa [$]
S -> .aFb [$]
S -> .bFa [$]
S -> .bEb [$]
(2)
S' -> S. [$]
(3)
S -> a.Ea [$]
S -> a.Fb [$]
E -> .e [a]
F -> .e [b]
(4)
E -> e. [a]
F -> e. [b]
(5)
S -> aE.a [$]
(6)
S -> aEa. [$]
(7)
S -> aF.b [$]
(8)
S -> aFb. [$]
(9)
S -> b.Fa [$]
S -> b.Eb [$]
E -> .e [b]
F -> .e [a]
(10)
E -> e. [b]
F -> e. [a]
(11)
S -> bF.a [$]
(12)
S -> bFa. [$]
(13)
S -> bE.b [$]
(14)
S -> bEb. [$]
If you'll notice, states (4) and (10) have the same core, so in the LALR(1) automaton we'd merge them together to form the new state
(4, 10)
E -> e. [a, b]
F -> e. [a, b]
Which now has a reduce/reduce conflict in it (all conflicts in LALR(1) that weren't present in the LR(1) parser are reduce/reduce, by the way). This accounts for why the grammar is LR(1) but not LALR(1).
Hope this helps!
answered Dec 13, 2011 at 21:12
templatetypedef
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8 Comments
Jan Vorcak
well, you helped me a lot, I realised one mistake a do in an analysis in my pdf, but anyway, I found this here and I wanted to prove it to my self, my result is also that it's a valid LARL(1) grammar, so I guess there is a mistake on that website? am I right?
templatetypedef
I guess that would be a mistake on the website, since we just built the LALR automaton and had
bison check it for us. I would assume that the intent was to find a LALR but not SLR grammar.Jan Vorcak
well, I figured it out, you miss rules E->e and F->e in your analysis, that's why
bison didn't have any error outputtemplatetypedef
@JanVorcak- Answer updated. Can you take a look at this and see if it explains things better?
Michael Mrozek
Is there a typo in the second line of state 10? It reads
E -> e. [a], I think it should be F -> e. [a] |