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A Perspective on Lindström Quantifiers and Oracles

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Book cover Generalized Quantifiers and Computation (ESSLLI 1997)

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Abstract

This paper presents a perspective on the relationship between Lindström quantifiers in model theory and oracle computations in complexity theory. We do not study this relationship here in full generality (indeed, there is much more work to do in order to obtain a full appreciation), but instead we examine what amounts to a thread of research in this topic running from the motivating results, concerning logical characterizations of nondeterministic polynomial-time, to the consideration of Lindström quantifiers as oracles, and through to the study of some naturally arising questions (and subsequent answers). Our presentation follows the chronological progress of the thread and highlights some important techniques and results at the interface between finite model theory and computational complexity theory.

Supported by EPSRC Grant GR/K 96564.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Leicester University, Leicester, LE1 7RH, UK

    Iain A. Stewart

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  1. Iain A. Stewart
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Helsinki, P.O. Box 4, Yliopistonkatu 5, 00014, Helsinki, Finland

    Jouko Väänänen

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© 1999 Springer-Verlag Berlin Heidelberg

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Stewart, I.A. (1999). A Perspective on Lindström Quantifiers and Oracles. In: Väänänen, J. (eds) Generalized Quantifiers and Computation. ESSLLI 1997. Lecture Notes in Computer Science, vol 1754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46583-9_3

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  • DOI: https://doi.org/10.1007/3-540-46583-9_3

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  • Print ISBN: 978-3-540-66993-7

  • Online ISBN: 978-3-540-46583-6

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