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Improved Composition Theorems for Functions and Relations

Authors Sajin Koroth , Or Meir

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Author Details

Sajin Koroth
  • Department of Computer Science, University of Haifa, Haifa 3498838, Israel
Or Meir
  • Department of Computer Science, University of Haifa, Haifa 3498838,Israel

Funding

  • Koroth, Sajin: Supported by the Israel Science Foundation (grant No. 1445/16)
  • Meir, Or: Partially supported by the Israel Science Foundation (grant No. 1445/16)

Cite As Get BibTex

Sajin Koroth and Or Meir. Improved Composition Theorems for Functions and Relations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.48

Abstract

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 NC^1. As an approach for this question, Karchmer, Raz and Wigderson [Mauricio Karchmer et al., 1995] proposed a conjecture called the KRW conjecture, which if true, would imply that P is not cotained in NC^{1}.
Since proving this conjecture is currently considered an extremely difficult problem, previous works by Edmonds, Impagliazzo, Rudich and Sgall [Edmonds et al., 2001], Håstad and Wigderson [Johan Håstad and Avi Wigderson, 1990] and Gavinsky, Meir, Weinstein and Wigderson [Dmitry Gavinsky et al., 2014] considered weaker variants of the conjecture. In this work we significantly improve the parameters in these variants, achieving almost tight lower bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Circuit complexity
  • Theory of computation → Complexity classes
Keywords
  • circuit complexity
  • communication complexity
  • KRW conjecture
  • composition

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References

  1. J. Edmonds, R. Impagliazzo, S. Rudich, and J. Sgall. Communication complexity towards lower bounds on circuit depth. computational complexity, 10(3):210-246, Dec 2001. URL: http://dx.doi.org/10.1007/s00037-001-8195-x.
  2. Dmitry Gavinsky, Or Meir, Omri Weinstein, and Avi Wigderson. Toward better formula lower bounds: an information complexity approach to the KRW composition conjecture. In Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 213-222, 2014. Google Scholar
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