{"title":"Automated construction of compound Markov chains from generalized stochastic high-level Petri nets","authors":"J.A. Carasco","doi":"10.1109/PNPM.1989.68543","DOIUrl":null,"url":null,"abstract":"A new type of Petri nets called generalized stochastic high-level Petri nets (GSHLPNs), combining the quantities of GSPNs and SHLPNs, is presented. The automated construction of compound continuous-time Markov chains (CTMCs) from GSHLPNs is also considered. A formalism for the description of compound markings allowing a symbolic firing of the net to obtain a compound CTMC with correct state group is derived. The construction of the compound CTMC requires an algorithm to test the equivalence of compound markings. I tis shown that, in the general case and for bounded number of rotation groups, the problem is polynomially equivalent to graph isomorphism, a problem whose classification in the NP world is currently open.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"224 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PNPM.1989.68543","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
A new type of Petri nets called generalized stochastic high-level Petri nets (GSHLPNs), combining the quantities of GSPNs and SHLPNs, is presented. The automated construction of compound continuous-time Markov chains (CTMCs) from GSHLPNs is also considered. A formalism for the description of compound markings allowing a symbolic firing of the net to obtain a compound CTMC with correct state group is derived. The construction of the compound CTMC requires an algorithm to test the equivalence of compound markings. I tis shown that, in the general case and for bounded number of rotation groups, the problem is polynomially equivalent to graph isomorphism, a problem whose classification in the NP world is currently open.<>
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