Random resolution refutations

0504571 - MÚ 2020 RIV CH eng J - Journal Article
Pudlák, Pavel - Thapen, Neil
Random resolution refutations.
Computational Complexity. Roč. 28, č. 2 (2019), s. 185-239. ISSN 1016-3328. E-ISSN 1420-8954
EU Projects: European Commission(XE) 339691 - FEALORA
Institutional support: RVO:67985840
Keywords : probabilistic proof * proof complexity * resolutions * witching lemma
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 0.850, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1007/s00037-019-00182-7

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.
Permanent Link: http://hdl.handle.net/11104/0296173