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Random resolution refutations
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SYSNO ASEP 0504571 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Random resolution refutations Tvůrce(i) Pudlák, Pavel (MU-W) RID, SAI
Thapen, Neil (MU-W) RID, SAIZdroj.dok. Computational Complexity. - : Springer - ISSN 1016-3328
Roč. 28, č. 2 (2019), s. 185-239Poč.str. 55 s. Jazyk dok. eng - angličtina Země vyd. CH - Švýcarsko Klíč. slova probabilistic proof ; proof complexity ; resolutions ; witching lemma Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Způsob publikování Omezený přístup Institucionální podpora MU-W - RVO:67985840 UT WOS 000467906700002 EID SCOPUS 85064660360 DOI 10.1007/s00037-019-00182-7 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2020 Elektronická adresa http://dx.doi.org/10.1007/s00037-019-00182-7
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