Pudlák, Pavel ;
Thapen, Neil
Random Resolution Refutations
Abstract
We study the random resolution refutation system definedin [Buss et al. 2014]. This attempts to capture the notion of a resolution refutation that may make mistakes but is correct most of the time. By proving the equivalence of several different definitions, we show that this concept is robust. On the other hand, if P does not equal NP, then random resolution cannot be polynomially simulated by any proof system in which correctness of proofs is checkable in polynomial time.
We prove several upper and lower bounds on the width and size of random resolution refutations of explicit and random unsatisfiable CNF formulas. Our main result is a separation between polylogarithmic width random resolution and quasipolynomial size resolution, which solves the problem stated in [Buss et al. 2014]. We also prove exponential size lower bounds on random resolution refutations of the pigeonhole principle CNFs, and of a family of CNFs which have polynomial size refutations in constant depth Frege.
BibTeX  Entry
@InProceedings{pudlk_et_al:LIPIcs:2017:7523,
author = {Pavel Pudl{\'a}k and Neil Thapen},
title = {{Random Resolution Refutations}},
booktitle = {32nd Computational Complexity Conference (CCC 2017)},
pages = {1:11:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770408},
ISSN = {18688969},
year = {2017},
volume = {79},
editor = {Ryan O'Donnell},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7523},
URN = {urn:nbn:de:0030drops75235},
doi = {10.4230/LIPIcs.CCC.2017.1},
annote = {Keywords: proof complexity, random, resolution}
}
2017
Keywords: 

proof complexity, random, resolution 
Seminar: 

32nd Computational Complexity Conference (CCC 2017)

Issue date: 

2017 
Date of publication: 

2017 