{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article9113","name":"Monadic Second Order Finite Satisfiability and Unbounded Tree-Width","abstract":"The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese. We prove that the following problem is decidable:\r\n\r\nInput: (i) A monadic second order logic sentence alpha, and (ii) a sentence beta in the two-variable fragment of first order logic extended with counting quantifiers. The vocabularies of alpha and beta may intersect.\r\n\r\nOutput: Is there a finite structure which satisfies alpha and beta such that the restriction of the structure to the vocabulary of alpha has bounded tree-width? (The tree-width of the desired structure is not bounded.)\r\n\r\nAs a consequence, we prove the decidability of the satisfiability problem by a finite structure of bounded tree-width of a logic MS^{exists card} extending monadic second order logic with linear cardinality constraints of the form |X_{1}|+...+|X_{r}| < |Y_{1}|+...+|Y_{s}| on the variables X_i, Y_j of the outer-most quantifier block. We prove the decidability of a similar extension of WS1S.","keywords":["Monadic Second Order Logic MSO","Two variable Fragment with Counting C2","Finite decidability","Unbounded Tree-width","WS1S with Cardinality Constraints"],"author":[{"@type":"Person","name":"Kotek, Tomer","givenName":"Tomer","familyName":"Kotek"},{"@type":"Person","name":"Veith, Helmut","givenName":"Helmut","familyName":"Veith"},{"@type":"Person","name":"Zuleger, Florian","givenName":"Florian","familyName":"Zuleger"}],"position":13,"pageStart":"13:1","pageEnd":"13:20","dateCreated":"2016-08-29","datePublished":"2016-08-29","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kotek, Tomer","givenName":"Tomer","familyName":"Kotek"},{"@type":"Person","name":"Veith, Helmut","givenName":"Helmut","familyName":"Veith"},{"@type":"Person","name":"Zuleger, Florian","givenName":"Florian","familyName":"Zuleger"}],"copyrightYear":"2016","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.CSL.2016.13","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6265","volumeNumber":62,"name":"25th EACSL Annual Conference on Computer Science Logic (CSL 2016)","dateCreated":"2016-08-29","datePublished":"2016-08-29","editor":[{"@type":"Person","name":"Talbot, Jean-Marc","givenName":"Jean-Marc","familyName":"Talbot"},{"@type":"Person","name":"Regnier, Laurent","givenName":"Laurent","familyName":"Regnier"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article9113","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6265"}}}