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On optimal heuristic randomized semidecision procedures, with application to proof complexity. / Hirsch, Edward A.; Itsykson, Dmitry.

STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science. 2010. p. 453-464 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 5).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Hirsch, EA & Itsykson, D 2010, On optimal heuristic randomized semidecision procedures, with application to proof complexity. in STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics, LIPIcs, vol. 5, pp. 453-464, 27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010, Nancy, France, 4/03/10. https://doi.org/10.4230/LIPIcs.STACS.2010.2475

APA

Hirsch, E. A., & Itsykson, D. (2010). On optimal heuristic randomized semidecision procedures, with application to proof complexity. In STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science (pp. 453-464). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 5). https://doi.org/10.4230/LIPIcs.STACS.2010.2475

Vancouver

Hirsch EA, Itsykson D. On optimal heuristic randomized semidecision procedures, with application to proof complexity. In STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science. 2010. p. 453-464. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.STACS.2010.2475

Author

Hirsch, Edward A. ; Itsykson, Dmitry. / On optimal heuristic randomized semidecision procedures, with application to proof complexity. STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science. 2010. pp. 453-464 (Leibniz International Proceedings in Informatics, LIPIcs).

BibTeX

@inproceedings{fdf6fbed4f004a23b765fe4ba7c49d3b,
title = "On optimal heuristic randomized semidecision procedures, with application to proof complexity",
abstract = "The existence of a (p-)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Kraj{\'i}{\v c}ek and Pudl{\'a}k [KP89] show that this question is equivalent to the existence of an algorithm that is optimal1 on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms do exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false {"}theorems{"} (according to any polynomial-time samplable distribution on non-tautologies) and err with bounded probability on other inputs. Our result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems.",
keywords = "Optimal algorithm, Propositional proof complexity",
author = "Hirsch, {Edward A.} and Dmitry Itsykson",
year = "2010",
month = dec,
day = "1",
doi = "10.4230/LIPIcs.STACS.2010.2475",
language = "English",
isbn = "9783939897163",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
pages = "453--464",
booktitle = "STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science",
note = "27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010 ; Conference date: 04-03-2010 Through 06-03-2010",

}

RIS

TY - GEN

T1 - On optimal heuristic randomized semidecision procedures, with application to proof complexity

AU - Hirsch, Edward A.

AU - Itsykson, Dmitry

PY - 2010/12/1

Y1 - 2010/12/1

N2 - The existence of a (p-)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal1 on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms do exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false "theorems" (according to any polynomial-time samplable distribution on non-tautologies) and err with bounded probability on other inputs. Our result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems.

AB - The existence of a (p-)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal1 on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms do exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false "theorems" (according to any polynomial-time samplable distribution on non-tautologies) and err with bounded probability on other inputs. Our result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems.

KW - Optimal algorithm

KW - Propositional proof complexity

UR - http://www.scopus.com/inward/record.url?scp=78650841667&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.STACS.2010.2475

DO - 10.4230/LIPIcs.STACS.2010.2475

M3 - Conference contribution

AN - SCOPUS:78650841667

SN - 9783939897163

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 453

EP - 464

BT - STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science

T2 - 27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010

Y2 - 4 March 2010 through 6 March 2010

ER -

ID: 49786774