Questions tagged [communication-complexity]
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6 questions
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relation between the approximate $\gamma_2$ norms of Boolean matrix and sign matrix
For a real matrix $A$, its $\gamma_2$-norm is defined as
$$\gamma_2(A)=\min_{X,Y:A=XY}||X||_{row}||Y||_{col},$$
where $||\cdot||_{row},||\cdot||_{col}$ are defined as the maximum $\ell_2$-norm of row ...
- 551
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Permutation of low circuit complexity
Let $\mathcal P$ be the set of permutations in $F_2^n$. I am interested in the circuit complexity of such functions in $AC^k[2]$ setup. What are the relevant upper and lower bounds in this context?
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Quantum versus classical communication complexity
Problem. Is it true that any 2-party communication problem $f(x,y)$ of poly-logarithmic complexity in the quantum simultaneous message passing model ($Q''$) has complexity $n^{o(1)}$ (i.e., strongly ...
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Entropy x Complexity - Shannon x Kolmogorov [closed]
This is a very common question but I think I’m posting it in a different way.
Suppose that we have 256 different possible messages with uniform distribution to be represented in a binary code. Then ...
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what is the largest gap between rank and approximate rank
$\epsilon$-approximation rank of a matrix $M$ is the minimum rank of a real matrix $A$ which differs from $M$ at most $\epsilon$ in each entry. Associating any function $f:X\times Y\rightarrow${1,-1} ...
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Space Bounded Communication Complexity of Identity
$\bf Definition.$ We define the space bounded communication in the following way. A and B are
supernatural beings capable of computing anything but
they only have a limited amount of memory and that ...
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