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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.48
URN: urn:nbn:de:0030-drops-94525
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9452/
Koroth, Sajin ; Meir, Or
Improved Composition Theorems for Functions and Relations
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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.
BibTeX - Entry
@InProceedings{koroth_et_al:LIPIcs:2018:9452,
author = {Sajin Koroth and Or Meir},
title = {{Improved Composition Theorems for Functions and Relations}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
pages = {48:1--48:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-085-9},
ISSN = {1868-8969},
year = {2018},
volume = {116},
editor = {Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9452},
URN = {urn:nbn:de:0030-drops-94525},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2018.48},
annote = {Keywords: circuit complexity, communication complexity, KRW conjecture, composition}
}
| Keywords: | circuit complexity, communication complexity, KRW conjecture, composition | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 13.08.2018 |
