{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:36:05Z","timestamp":1753889765230,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,12,11]],"date-time":"2015-12-11T00:00:00Z","timestamp":1449792000000},"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 prove that the model checking problem for the existential fragment of\nfirst-order (FO) logic on partially ordered sets is fixed-parameter tractable\n(FPT) with respect to the formula and the width of a poset (the maximum size of\nan antichain). While there is a long line of research into FO model checking on\ngraphs, the study of this problem on posets has been initiated just recently by\nBova, Ganian and Szeider (CSL-LICS 2014), who proved that the existential\nfragment of FO has an FPT algorithm for a poset of fixed width. We improve upon\ntheir result in two ways: (1) the runtime of our algorithm is\nO(f(|{\\phi}|,w).n^2) on n-element posets of width w, compared to O(g(|{\\phi}|).\nn^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow.\nWe complement this result by showing that, under a certain\ncomplexity-theoretical assumption, the existential FO model checking problem\ndoes not have a polynomial kernel.<\/jats:p>","DOI":"10.2168\/lmcs-11(4:8)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:40Z","timestamp":1479736000000},"source":"Crossref","is-referenced-by-count":1,"title":["Faster Existential FO Model Checking on Posets"],"prefix":"10.46298","volume":"Volume 11, Issue 4","author":[{"given":"Jakub","family":"Gajarsk\u00fd","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2125-1514","authenticated-orcid":false,"given":"Petr","family":"Hlin\u011bn\u00fd","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Obdr\u017e\u00e1lek","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1935-651X","authenticated-orcid":false,"given":"Sebastian","family":"Ordyniak","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,12,11]]},"reference":[{"key":"1124:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1609\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1609\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:07:46Z","timestamp":1681243666000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1609"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,11]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(4:8)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1409.4433","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1409.4433","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,12,11]]},"article-number":"1609"}}