{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T18:30:20Z","timestamp":1781893820272,"version":"3.54.5"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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, F\u00fcrer, 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.<\/jats:p>","DOI":"10.2178\/jsl\/1190150152","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:14:26Z","timestamp":1197573266000},"page":"1093-1125","source":"Crossref","is-referenced-by-count":39,"title":["On polynomial time computation over unordered structures"],"prefix":"10.1017","volume":"67","author":[{"given":"Andreas","family":"Blass","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuri","family":"Gurevich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009452_ref020","first-page":"137","volume-title":"Proceedings of the 14th ACM Symposium on Theory of Computing","author":"Vardi","year":"1982"},{"key":"S0022481200009452_ref019","first-page":"72","volume-title":"Computer Science Logic 2000","volume":"1862","author":"Shelah","year":"2000"},{"key":"S0022481200009452_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21676-7"},{"key":"S0022481200009452_ref016","unstructured":"Huggins J. K. , ASM Michigan Web page, http:\/\/www.eecs.umich.edu\/gasm\/."},{"key":"S0022481200009452_ref014","first-page":"233","volume-title":"Bulletin of the European Association on Theoretical Computer Science","volume":"63","author":"Gurevich","year":"1997"},{"key":"S0022481200009452_ref015","first-page":"549","volume":"61","author":"Gurevich","year":"1996","journal-title":"On finite rigid structures"},{"key":"S0022481200009452_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(86)80029-8"},{"key":"S0022481200009452_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(82)90012-5"},{"key":"S0022481200009452_ref012","first-page":"1","volume-title":"Current trends in theoretical computer science","author":"Gurevich","year":"1988"},{"key":"S0022481200009452_ref011","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1997.2675"},{"key":"S0022481200009452_ref003","doi-asserted-by":"publisher","DOI":"10.1137\/0213042"},{"key":"S0022481200009452_ref001","first-page":"209","volume-title":"Proceedings of the 23rd ACM Symposium on Theory of Computing","author":"Abiteboul","year":"1991"},{"key":"S0022481200009452_ref002","unstructured":"Blass A. and Gurevich Y. , Strong extension axioms and Shelah's zero-one law for choiceless polynomial time, to appear."},{"key":"S0022481200009452_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-13331-3_31"},{"key":"S0022481200009452_ref005","first-page":"22","volume-title":"Information and Computation","volume":"1912","author":"Blass","year":"2000"},{"key":"S0022481200009452_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00005-6"},{"key":"S0022481200009452_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9967-7"},{"key":"S0022481200009452_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01305232"},{"key":"S0022481200009452_ref010","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1998.2712"},{"key":"S0022481200009452_ref013","first-page":"9","volume-title":"Specification and validation methods","author":"Gurevich","year":"1995"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009452","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:45:45Z","timestamp":1557189945000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009452\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009452"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150152","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}