Optimal acceptors and optimal proof systems

Edward A. Hirsch

doi:10.1007/978-3-642-13562-0_4

Optimal acceptors and optimal proof systems

Edward A. Hirsch

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

9 Scopus citations

Abstract

Unless we resolve the P vs NP question, we are unable to say whether there is an algorithm (acceptor) that accepts Boolean tautologies in polynomial time and does not accept non-tautologies (with no time restriction). Unless we resolve the co-NP vs NP question, we are unable to say whether there is a proof system that has a polynomial-size proof for every tautology. In such a situation, it is typical for complexity theorists to search for "universal" objects; here, it could be the "fastest" acceptor (called optimal acceptor) and a proof system that has the "shortest" proof (called optimal proof system) for every tautology. Neither of these objects is known to the date. In this survey we review the connections between these questions and generalizations of acceptors and proof systems that lead or may lead to universal objects.

Original language	English
Title of host publication	Theory and Applications of Models of Computation - 7th Annual Conference, TAMC 2010, Proceedings
Pages	28-39
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-13562-0_4
State	Published - 2010
Externally published	Yes
Event	7th Annual Conference on Theory and Applications of Models of Computation, TAMC 2010 - Prague, Czech Republic Duration: 7 Jun 2010 → 11 Jun 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6108 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th Annual Conference on Theory and Applications of Models of Computation, TAMC 2010
Country/Territory	Czech Republic
City	Prague
Period	7/06/10 → 11/06/10

Access to Document

10.1007/978-3-642-13562-0_4

Cite this

Hirsch, E. A. (2010). Optimal acceptors and optimal proof systems. In Theory and Applications of Models of Computation - 7th Annual Conference, TAMC 2010, Proceedings (pp. 28-39). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6108 LNCS). https://doi.org/10.1007/978-3-642-13562-0_4

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Hirsch, EA 2010, Optimal acceptors and optimal proof systems. in Theory and Applications of Models of Computation - 7th Annual Conference, TAMC 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6108 LNCS, pp. 28-39, 7th Annual Conference on Theory and Applications of Models of Computation, TAMC 2010, Prague, Czech Republic, 7/06/10. https://doi.org/10.1007/978-3-642-13562-0_4

Optimal acceptors and optimal proof systems. / Hirsch, Edward A.
Theory and Applications of Models of Computation - 7th Annual Conference, TAMC 2010, Proceedings. 2010. p. 28-39 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6108 LNCS).

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

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Optimal acceptors and optimal proof systems

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