{"title":"分解量化合取(或析取)公式","authors":"Hubie Chen, V. Dalmau","doi":"10.1109/LICS.2012.31","DOIUrl":null,"url":null,"abstract":"Model checking-deciding if a logical sentence holds on a structure-is a basic computational task that is well-known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":"{\"title\":\"Decomposing Quantified Conjunctive (or Disjunctive) Formulas\",\"authors\":\"Hubie Chen, V. Dalmau\",\"doi\":\"10.1109/LICS.2012.31\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Model checking-deciding if a logical sentence holds on a structure-is a basic computational task that is well-known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.\",\"PeriodicalId\":407972,\"journal\":{\"name\":\"2012 27th Annual IEEE Symposium on Logic in Computer Science\",\"volume\":\"57 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 27th Annual IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2012.31\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 27th Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2012.31","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Model checking-deciding if a logical sentence holds on a structure-is a basic computational task that is well-known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.