Deterministic communication complexity vs partition number
Background: Consider the usual two-party model of communication complexity where Alice and Bob are given $n$-bit strings $x$ and $y$ and have to compute some Boolean function $f(x,y)$, where $f:{0,1}^n...
View ArticleOn the notion of positive rank of a matrix
The positive rank of a square matrix is defined in Theorem $3$ of “Expressing Combinatorial Optimization Problems by Linear Programs” by Mihalis Yannakakis as follows: given a $ntimes n$ matrix $A$,...
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The relationship between QCMA and QMA in the Turing and Communication model
First my background about computational complexity is still beginner. Recent paper published by Klauck and Podder [KP14] show that for the first time an exponential gap between computing partial...
View ArticleResearch problems in communication complexity
There have been many open challenges questions in this forum. For instance, Research and open challenges in Programming Language Theory What are current open problems in compiler theory? Outstanding...
View ArticleOn connecting combinatorial rectangles
In communication complexity one important object is the combinatorial retangle. Given a $0-1$ square matrix $M$, do their exist permutations $sigma,pi$ such that $sigma Mpi$ consists of only geometric...
View ArticleLow rank Log rank conjecture
What is known about log rank conjecture in special situations of $O(log N)$ rank $0/1$ matrix of size $Ntimes N$? Is there at least a conditional result showing better than $O(sqrt{log N})$ bound?
View ArticleMinimum communication cost for zero knowledge proofs of three colorability
Goldreich et al.’s proof that three colorability has zero knowledge proofs uses bit commitment for an entire coloring of the graph in each round [1]. If a graph has $n$ vertices and $e$ edges, a secure...
View ArticleModern tools deterministic communication applications
Partition number, Fooling-set method along with rank method provide important tools to identify deterministic communication complexity of a function. These techniques were identified some decades...
View ArticleInformation complexity of query algorithms?
Information complexity has been a very useful tool in communication complexity, mainly used to lower bound the communication complexity of distributed problems. Is there an analogue of information...
View ArticleA direct-sum theorem for the non-deterministic communication complexity of...
A non-deterministic protocol for the inequality function is a protocol that behaves as follows: Alice and Bob get strings $x,yin{0,1}^n$ respectively, and an untrusted prover is trying to convince them...
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