{"title":"Equilibrium and Termination","authors":"V. Danos, N. Oury","doi":"10.4204/EPTCS.26.7","DOIUrl":null,"url":null,"abstract":"We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"63 1","pages":"75-84"},"PeriodicalIF":0.0000,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dialogues in cardiovascular medicine : DCM","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.26.7","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
We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.
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