How to construct random functions
Journal of the ACM (JACM)
Acta Informatica
Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A simple lower bound for monotone clique using a communication game
Information Processing Letters
Monotone circuits for matching require linear depth
Journal of the ACM (JACM)
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Communication complexity
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Proceedings of the 18th Conference on Foundations of Software Technology and Theoretical Computer Science
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Number-theoretic constructions of efficient pseudo-random functions
Journal of the ACM (JACM)
Introduction to Coding Theory
Communication in the presence of replication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algebrization: a new barrier in complexity theory
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Complexity Lower Bounds using Linear Algebra
Foundations and Trends® in Theoretical Computer Science
Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Note: Some improved bounds on communication complexity via new decomposition of cliques
Discrete Applied Mathematics
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We consider the following question: given a two-argument boolean function f, represented as an N x N binary matrix, how hard is it to determine the (deterministic) communication complexity of f? We address two aspects of this question. On the computational side, we prove that, under appropriate cryptographic assumptions (such as the intractability of factoring), the deterministic communication complexity of f is hard to approximate to within some constant. Under stronger (yet arguably reasonable) assumptions, we obtain even stronger hardness results that match the best known approximation. On the analytic side, we present a family of (two-argument) functions for which determining the deterministic communication complexity (or even obtaining non-trivial lower bounds on it) implies proving circuit lower bounds for some related functions. Such connections between circuit complexity and communication complexity were known before (Karchmer &#; Wigderson, 1988) only in the more involved context of relations (search problems) but not in the context of functions (decision problems). This result, in particular, may explain the difficulty of analyzing the communication complexity of certain functions such as the "clique vs. independent-set" family of functions, introduced by Yannakakis (1988).