Journal of Symbolic Logic 67 (3):1093-1125 (2002)

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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DOI 10.2178/jsl/1190150152
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References found in this work BETA

Choiceless Polynomial Time.Andreas Blass, Yuri Gurevich & Saharon Shelah - 1999 - Annals of Pure and Applied Logic 100 (1-3):141-187.
On Finite Rigid Structures.Yuri Gurevich & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (2):549-562.

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Citations of this work BETA

Symbioses Between Mathematical Logic and Computer Science.Andreas Blass - 2016 - Annals of Pure and Applied Logic 167 (10):868-878.

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