On the computational complexity of finding hard tautologies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287302" target="_blank" >RIV/00216208:11320/14:10287302 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985840:_____/14:00430340

Výsledek na webu

<a href="http://dx.doi.org/10.1112/blms/bdt071" target="_blank" >http://dx.doi.org/10.1112/blms/bdt071</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/blms/bdt071" target="_blank" >10.1112/blms/bdt071</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the computational complexity of finding hard tautologies

Popis výsledku v původním jazyce

It is well known (cf. Krajicek and Pudlak ['Propositional proof systems, the consistency of first order theories and the complexity of computations', J. Symbolic Logic 54 (1989) 1063-1079]) that a polynomial time algorithm finding tautologies hard for apropositional proof system P exists if and only if P is not optimal. Such an algorithm takes 1((k)) and outputs a tautology tau(k) of size at least k such that P is not p-bounded on the set of all formulas tau(k). We consider two more general search problems involving finding a hard formula, Cert and Find, motivated by two hypothetical situations: that one can prove that NP not equal coNP and that no optimal proof system exists. In Cert one is asked to find a witness that a given non-deterministic circuit with k inputs does not define TAUT boolean AND{0, 1}(k). In Find, given 1((k)) and a tautology alpha of size at most k(0)(c), one should output a size k tautology beta that has no size k(1)(c) P-proof from substitution instances of alp

Název v anglickém jazyce

On the computational complexity of finding hard tautologies

Popis výsledku anglicky

It is well known (cf. Krajicek and Pudlak ['Propositional proof systems, the consistency of first order theories and the complexity of computations', J. Symbolic Logic 54 (1989) 1063-1079]) that a polynomial time algorithm finding tautologies hard for apropositional proof system P exists if and only if P is not optimal. Such an algorithm takes 1((k)) and outputs a tautology tau(k) of size at least k such that P is not p-bounded on the set of all formulas tau(k). We consider two more general search problems involving finding a hard formula, Cert and Find, motivated by two hypothetical situations: that one can prove that NP not equal coNP and that no optimal proof system exists. In Cert one is asked to find a witness that a given non-deterministic circuit with k inputs does not define TAUT boolean AND{0, 1}(k). In Find, given 1((k)) and a tautology alpha of size at most k(0)(c), one should output a size k tautology beta that has no size k(1)(c) P-proof from substitution instances of alp

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/IAA100190902" target="_blank" >IAA100190902: Matematická logika, složitost a algoritmy</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Bulletin of the London Mathematical Society

ISSN

0024-6093

e-ISSN

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Svazek periodika

2014

Číslo periodika v rámci svazku

46

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

111-125

Kód UT WoS článku

000330193400011

EID výsledku v databázi Scopus

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