Improved Composition Theorems for Functions and Relations

Sajin Koroth, Or Meir, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
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 N C 1 . 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 N C 1 . Since proving this conjecture is currently considered an extremely difficult problem, previous works by Edmonds, Impagliazzo, Rudich and
more » ... [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.
doi:10.4230/lipics.approx-random.2018.48 dblp:conf/approx/KorothM18 fatcat:sapv2l5y45hedfbcaho2qr7cgm