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A perspective on Lindström quantifiers and oracles.

Stewart, I. A. (1999) 'A perspective on Lindström quantifiers and oracles.', in 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. Berlin: Springer, pp. 51-71. Lecture notes in computer science. (1754).


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.

Item Type:Book chapter
Keywords:Finite model theory, Descriptive complexity, Lindström quantifiers, Oracles.
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:28 June 2010
Date of first online publication:1999
Date first made open access:No date available

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