A perspective on Lindström quantifiers and oracles

Stewart, I.A.

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: Jun 28, 2010
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1662212
• Publisher URL: http://www.dur.ac.uk/i.a.stewart/Papers/perspective.ps