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September 2002 On polynomial time computation over unordered structures
Andreas Blass, Yuri Gurevich, Saharon Shelah
J. Symbolic Logic 67(3): 1093-1125 (September 2002). DOI: 10.2178/jsl/1190150152

Abstract

This paper is motivated by the question whether there exists a logic capturing polynomial time computation over unordered structures. We consider several algorithmic problems near the border of the known, logically defined complexity classes contained in polynomial time. We show that fixpoint logic plus counting is stronger than might be expected, in that it can express the existence of a complete matching in a bipartite graph. We revisit the known examples that separate polynomial time from fixpoint plus counting. We show that the examples in a paper of Cai, Fürer, and Immerman, when suitably padded, are in choiceless polynomial time yet not in fixpoint plus counting. Without padding, they remain in polynomial time but appear not to be in choiceless polynomial time plus counting. Similar results hold for the multipede examples of Gurevich and Shelah, except that their final version of multipedes is, in a sense, already suitably padded. Finally, we describe another possible candidate, involving determinants, for the task of separating polynomial time from choiceless polynomial time plus counting.

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Andreas Blass. Yuri Gurevich. Saharon Shelah. "On polynomial time computation over unordered structures." J. Symbolic Logic 67 (3) 1093 - 1125, September 2002. https://doi.org/10.2178/jsl/1190150152

Information

Published: September 2002
First available in Project Euclid: 18 September 2007

zbMATH: 1020.03038
MathSciNet: MR1926601
Digital Object Identifier: 10.2178/jsl/1190150152

Subjects:
Primary: 68Q19
Secondary: 03B70 , 03C13 , 03D15

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.67 • No. 3 • September 2002
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