On the computational complexity of finding hard tautologies

Result code in 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>
Alternative codes found
RIV/67985840:_____/14:00430340
Result on the web
<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>

Result language
angličtina
Original language name
On the computational complexity of finding hard tautologies
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/IAA100190902" target="_blank" >IAA100190902: Mathematical logic, complexity, and algorithms</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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