Improved Composition Theorems for Functions and Relations

One of the central problems in complexity theory is to prove super-logarithmic depth bounds for circuits computing a problem in P , i.e., to prove that P is not contained in NC1. As an approach for this question, Karchmer, Raz and Wigderson [5] proposed a conjecture called the KRW conjecture, which if true, would imply that P is not cotained in NC1. Since proving this conjecture is currently considered an extremely difficult problem, previous works by Edmonds, Impagliazzo, Rudich and Sgall [1], Håstad and Wigderson [3] and Gavinsky, Meir, Weinstein and Wigderson [2] considered weaker variants of the conjecture. In this work we significantly improve the parameters in these variants, achieving almost tight lower bounds. 2012 ACM Subject Classification Theory of computation → Communication complexity, Theory of computation → Circuit complexity, Theory of computation → Complexity classes

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