{"title":"一个可确定的微积分:初步报告","authors":"V. Pratt","doi":"10.1109/SFCS.1981.4","DOIUrl":null,"url":null,"abstract":"We describe a mu-calculus which amounts to modal logic plus a minimization operator, and show that its satisfiability problem is decidable in exponential time. This result subsumes corresponding results for propositional dynamic logic with test and converse, thus supplying a better setting for those results. It also encompasses similar results for a logic of flowgraphs. This work provides an intimate link between PDL as defined by the Segerberg axioms and the mu-calculi of de Bakker and Park.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"95","resultStr":"{\"title\":\"A decidable mu-calculus: Preliminary report\",\"authors\":\"V. Pratt\",\"doi\":\"10.1109/SFCS.1981.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe a mu-calculus which amounts to modal logic plus a minimization operator, and show that its satisfiability problem is decidable in exponential time. This result subsumes corresponding results for propositional dynamic logic with test and converse, thus supplying a better setting for those results. It also encompasses similar results for a logic of flowgraphs. This work provides an intimate link between PDL as defined by the Segerberg axioms and the mu-calculi of de Bakker and Park.\",\"PeriodicalId\":224735,\"journal\":{\"name\":\"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1981-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"95\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1981.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1981.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We describe a mu-calculus which amounts to modal logic plus a minimization operator, and show that its satisfiability problem is decidable in exponential time. This result subsumes corresponding results for propositional dynamic logic with test and converse, thus supplying a better setting for those results. It also encompasses similar results for a logic of flowgraphs. This work provides an intimate link between PDL as defined by the Segerberg axioms and the mu-calculi of de Bakker and Park.
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