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Optimal Acceptors and Optimal Proof Systems

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Theory and Applications of Models of Computation (TAMC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6108))

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.

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Authors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St. Petersburg, 191023, Russia

    Edward A. Hirsch

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  1. Edward A. Hirsch
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Editors and Affiliations

  1. Charles University, Malostranske nam 25, 11800, Praha 1, Czech Republic

    Jan Kratochvíl , Jiří Fiala  & Petr Kolman ,  & 

  2. State Key Lab. of Computer Science, Institute of Software,, Chinese Academy of Sciences, 100190, Beijing, P.R. China

    Angsheng Li

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Hirsch, E.A. (2010). Optimal Acceptors and Optimal Proof Systems. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-13562-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13561-3

  • Online ISBN: 978-3-642-13562-0

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