Facundo Carreiro, Alessandro Facchini, Y. Venema, F. Zanasi
{"title":"Weak MSO: automata and expressiveness modulo bisimilarity","authors":"Facundo Carreiro, Alessandro Facchini, Y. Venema, F. Zanasi","doi":"10.1145/2603088.2603101","DOIUrl":null,"url":null,"abstract":"We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal μ-calculus where the application of the least fixpoint operator μp.φ is restricted to formulas φ that are continuous in p. Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE1∞ that is the extension of first-order logic with a generalized quantifier ∃∞, where ∃∞x.φ means that there are infinitely many objects satisfying φ. An important part of our work consists of a model-theoretic analysis of FOE1∞.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2603088.2603101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal μ-calculus where the application of the least fixpoint operator μp.φ is restricted to formulas φ that are continuous in p. Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE1∞ that is the extension of first-order logic with a generalized quantifier ∃∞, where ∃∞x.φ means that there are infinitely many objects satisfying φ. An important part of our work consists of a model-theoretic analysis of FOE1∞.