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Fields of Logic and Computation II pp 193–209Cite as

Is Polynomial Time Choiceless?

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9300))

Abstract

A long time ago, Yuri Gurevich made precise the problem of whether there is a logic capturing polynomial-time on arbitrary finite structures, and conjectured that no such logic exists. This conjecture is still open. Nevertheless, together with Andreas Blass and Saharon Shelah, he has also proposed what still seems to be the most promising candidate for a logic for polynomial time, namely Choiceless Polynomial Time (with counting). We survey some recent results on this logic.

For Yuri Gurevich on the occasion of his 75th birthday.

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Notes

  1. 1.

    Structures are always assumed to be finite in this paper, with the exception of the herditarily finite expansions introduced in Sect. 2.

  2. 2.

    Actually, Gurevich and Shelah introduced a number of different variants of multipedes. What we use here are called 3-multipedes with shoes in [7].

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Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Erich Grädel & Martin Grohe

Authors
  1. Erich Grädel
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  2. Martin Grohe
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Correspondence to Erich Grädel .

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Editors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    Lev D. Beklemishev

  2. University of Michigan, Ann Arbor, Michigan, USA

    Andreas Blass

  3. Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  4. Universität des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

  5. Microsoft Research, REDMOND, Washington, USA

    Wolfram Schulte

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Grädel, E., Grohe, M. (2015). Is Polynomial Time Choiceless?. In: Beklemishev, L., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds) Fields of Logic and Computation II. Lecture Notes in Computer Science(), vol 9300. Springer, Cham. https://doi.org/10.1007/978-3-319-23534-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-23534-9_11

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  • Online ISBN: 978-3-319-23534-9

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