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We study projective dimension, a graph parameter, denoted by pd(G) for a bipartite graph G, introduced by Pudlák and Rödl (1992). For a Boolean function f (on n bits), Pudlák and Rödl associated a bipartite graph Gf and showed that size of the optimal branching program computing f, denoted by...
We introduce an idea called anti-gadgets for reductions in complexity theory. These anti-gadgets are presented as graph fragments, but their effect is equivalent to erasing the presence of other graph fragments, as if we had managed to include a negative copy of a certain graph gadget. We use...
We introduce a new information-theoretic measure, which we call Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of randomness they require in the context of...
We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef , we show a simple way to reduce...
We study limitations of polynomials computed by depth-2 circuits built over read-once formulas (ROFs). In particular: We prove a 2(n) lower bound for the sum of ROFs computing the 2n-variate polynomial in VP defined by Raz and Yehudayoff 21. We obtain a 2(√n) lower bound on the size of n1/15...
Given a graph G and a pair (F1, F2) of graph families, the function GDISJG,F1,F2 takes as input, two induced subgraphs G1 and G2 of G, such that G1 F1 and G2 F2 and returns 1 if V(G1) V(G2)= and 0 otherwise. We study the communication complexity of this problem in the two-party model. In...
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