{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:39:34Z","timestamp":1753889974656,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2016,6,23]],"date-time":"2016-06-23T00:00:00Z","timestamp":1466640000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We study the finite satisfiability problem for the two-variable fragment of\nfirst-order logic extended with counting quantifiers (C2) and interpreted over\nlinearly ordered structures. We show that the problem is undecidable in the\ncase of two linear orders (in the presence of two other binary symbols). In the\ncase of one linear order it is NEXPTIME-complete, even in the presence of the\nsuccessor relation. Surprisingly, the complexity of the problem explodes when\nwe add one binary symbol more: C2 with one linear order and in the presence of\nother binary predicate symbols is equivalent, under elementary reductions, to\nthe emptiness problem for multicounter automata.<\/jats:p>","DOI":"10.2168\/lmcs-12(2:8)2016","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:47:33Z","timestamp":1479736053000},"source":"Crossref","is-referenced-by-count":3,"title":["Two-variable Logic with Counting and a Linear Order"],"prefix":"10.46298","volume":"Volume 12, Issue 2","author":[{"given":"Witold","family":"Charatonik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1908-0827","authenticated-orcid":false,"given":"Piotr","family":"Witkowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2016,6,23]]},"reference":[{"key":"1213:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1640\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1640\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:08:42Z","timestamp":1681243722000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1640"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,23]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-12(2:8)2016","relation":{"is-same-as":[{"id-type":"arxiv","id":"1604.06038","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1604.06038","asserted-by":"subject"}],"is-part-of":[{"id-type":"doi","id":"10.4230\/lipics.csl.2015","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2016,6,23]]},"article-number":"1640"}}