Random resolution refutations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00504571" target="_blank" >RIV/67985840:_____/19:00504571 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00037-019-00182-7" target="_blank" >http://dx.doi.org/10.1007/s00037-019-00182-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00037-019-00182-7" target="_blank" >10.1007/s00037-019-00182-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Random resolution refutations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Random resolution refutations

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computational Complexity

ISSN

1016-3328

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

55

Strana od-do

185-239

Kód UT WoS článku

000467906700002

EID výsledku v databázi Scopus

2-s2.0-85064660360