{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10533","name":"A Dichotomy Theorem for the Inverse Satisfiability Problem","abstract":"The inverse satisfiability problem over a set of Boolean relations Gamma (Inv-SAT(Gamma)) is the computational decision problem of, given a set of models R, deciding whether there exists a SAT(Gamma) instance with R as its set of models. This problem is co-NP-complete in general and a dichotomy theorem for finite \u0393 containing the constant Boolean relations was obtained by Kavvadias and Sideri. In this paper we remove the latter condition and prove that Inv-SAT(Gamma) is always either tractable or co-NP-complete for all finite sets of relations Gamma, thus solving a problem open since 1998. Very little of the techniques used by Kavvadias and Sideri are applicable and we have to turn to more recently developed algebraic approaches based on partial polymorphisms. We also consider the case when \u0393 is infinite, where the situation differs markedly from the case of SAT. More precisely, we show that there exists infinite Gamma such that Inv-SAT(Gamma) is tractable even though there exists finite Delta is subset of Gamma such that Inv-SAT(Delta) is co-NP-complete.","keywords":["Complexity Theory","Inverse Satisfiability","Clone Theory"],"author":[{"@type":"Person","name":"Lagerkvist, Victor","givenName":"Victor","familyName":"Lagerkvist"},{"@type":"Person","name":"Roy, Biman","givenName":"Biman","familyName":"Roy"}],"position":39,"pageStart":"39:1","pageEnd":"39:14","dateCreated":"2018-02-12","datePublished":"2018-02-12","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Lagerkvist, Victor","givenName":"Victor","familyName":"Lagerkvist"},{"@type":"Person","name":"Roy, Biman","givenName":"Biman","familyName":"Roy"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2017.39","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":"http:\/\/dx.doi.org\/10.1016\/j.jcss.2008.02.005","isPartOf":{"@type":"PublicationVolume","@id":"#volume6296","volumeNumber":93,"name":"37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)","dateCreated":"2018-02-12","datePublished":"2018-02-12","editor":[{"@type":"Person","name":"Lokam, Satya","givenName":"Satya","familyName":"Lokam"},{"@type":"Person","name":"Ramanujam, R.","givenName":"R.","familyName":"Ramanujam"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10533","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":"#volume6296"}}}