Sh:760

• Blass, A. R., Gurevich, Y., & Shelah, S. (2002). On polynomial time computation over unordered structures. J. Symbolic Logic, 67(3), 1093–1125. arXiv: math/0102059 DOI: 10.2178/jsl/1190150152 MR: 1926601
• 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 plausible candidate, involving determinants, for the task of separating polynomial time from choiceless polynomial time plus counting.
• Version 2001-02-06_11 (46p) published version (34p)

@article{Sh:760,
 author = {Blass, Andreas R. and Gurevich, Yuri and Shelah, Saharon},
 title = {{On polynomial time computation over unordered structures}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {67},
 number = {3},
 year = {2002},
 pages = {1093--1125},
 issn = {0022-4812},
 mrnumber = {1926601},
 mrclass = {68Q19 (03B70 03C13 03D15)},
 doi = {10.2178/jsl/1190150152},
 note = {\href{https://arxiv.org/abs/math/0102059}{arXiv: math/0102059}},
 arxiv_number = {math/0102059}
}