{"title":"Forward Analysis for WSTS, Part III: Karp-Miller Trees","authors":"Michael Blondin, A. Finkel, J. Goubault-Larrecq","doi":"10.23638/LMCS-16(2:13)2020","DOIUrl":null,"url":null,"abstract":"This paper is a sequel of \"Forward Analysis for WSTS, Part I: Completions\" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and \"Forward Analysis for WSTS, Part II: Complete WSTS\" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downward-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural effectiveness assumptions, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Software Technology and Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23638/LMCS-16(2:13)2020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downward-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural effectiveness assumptions, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks.