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Random resolution refutations
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SYSNO ASEP 0504571 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Random resolution refutations Author(s) Pudlák, Pavel (MU-W) RID, SAI
Thapen, Neil (MU-W) RID, SAISource Title Computational Complexity. - : Springer - ISSN 1016-3328
Roč. 28, č. 2 (2019), s. 185-239Number of pages 55 s. Language eng - English Country CH - Switzerland Keywords probabilistic proof ; proof complexity ; resolutions ; witching lemma Subject RIV IN - Informatics, Computer Science OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000467906700002 EID SCOPUS 85064660360 DOI 10.1007/s00037-019-00182-7 Annotation We study the random resolution refutation system defined in Buss et al. (J Symb Logic 79(2):496–525, 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≠ 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2020 Electronic address http://dx.doi.org/10.1007/s00037-019-00182-7
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