{"title":"Towards a Classification of Behavioural Equivalences in Continuous-time Markov Processes","authors":"Linan Chen , Florence Clerc , Prakash Panangaden","doi":"10.1016/j.entcs.2020.09.004","DOIUrl":null,"url":null,"abstract":"<div><p>Bisimulation is a concept that captures behavioural equivalence of states in a transition system. In [Linan Chen, Florence Clerc, and Prakash Panangaden, Bisimulation for feller-dynkin processes, in: Proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics, Electronic Notes in Theoretical Computer Science 347 (2019) 45–63.], we proposed two equivalent definitions of bisimulation on continuous-time stochastic processes where the evolution is a <em>flow</em> through time. In the present paper, we develop the theory further: we introduce different concepts that correspond to different behavioural equivalences and compare them to bisimulation. In particular, we study the relation between bisimulation and symmetry groups of the dynamics. We also provide a game interpretation for two of the behavioural equivalences. We then compare those notions to their discrete-time analogues.</p></div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"352 ","pages":"Pages 53-77"},"PeriodicalIF":0.0000,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2020.09.004","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571066120300505","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Computer Science","Score":null,"Total":0}
引用次数: 1
Abstract
Bisimulation is a concept that captures behavioural equivalence of states in a transition system. In [Linan Chen, Florence Clerc, and Prakash Panangaden, Bisimulation for feller-dynkin processes, in: Proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics, Electronic Notes in Theoretical Computer Science 347 (2019) 45–63.], we proposed two equivalent definitions of bisimulation on continuous-time stochastic processes where the evolution is a flow through time. In the present paper, we develop the theory further: we introduce different concepts that correspond to different behavioural equivalences and compare them to bisimulation. In particular, we study the relation between bisimulation and symmetry groups of the dynamics. We also provide a game interpretation for two of the behavioural equivalences. We then compare those notions to their discrete-time analogues.
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