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A perspective on Lindström quantifiers and oracles

Stewart, I.A.

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Contributors

J. Väänänen
Editor

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.

Citation

Stewart, I. (1999). A perspective on Lindström quantifiers and oracles. In J. Väänänen (Ed.), Generalized quantifiers and computation : 9th European Summer School in Logic, Language, and Information ESSLLI’97 Workshop, 11-22 August 1997, Aix-en-Provence, France ; revised lectures (51-71). Springer Verlag. https://doi.org/10.1007/3-540-46583-9_3

Publication Date Jan 1, 1999
Deposit Date Jun 28, 2010
Publicly Available Date Mar 28, 2024
Publisher Springer Verlag
Pages 51-71
Series Title Lecture notes in computer science
Book Title Generalized quantifiers and computation : 9th European Summer School in Logic, Language, and Information ESSLLI’97 Workshop, 11-22 August 1997, Aix-en-Provence, France ; revised lectures.
ISBN 9783540669937
DOI https://doi.org/10.1007/3-540-46583-9_3
Keywords Finite model theory, Descriptive complexity, Lindström quantifiers, Oracles.
Publisher URL http://www.dur.ac.uk/i.a.stewart/Papers/perspective.ps

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