Abstract
AbstractBisimulation is a concept that captures behavioural equivalence of states in a variety of types of transition systems. It has been widely studied in a discrete-time setting. The core of this work is to generalise the discrete-time picture to continuous time by providing a notion of behavioural equivalence for continuous-time Markov processes. In Chen et al. [(2019). Electronic Notes in Theoretical Computer Science347 45–63.], we proposed two equivalent definitions of bisimulation for continuous-time stochastic processes where the evolution is a flow through time: the first one as an equivalence relation and the second one as a cospan of morphisms. In Chen et al. [(2020). Electronic Notes in Theoretical Computer Science.], we developed the theory further: we introduced different concepts that correspond to different behavioural equivalences and compared them to bisimulation. In particular, we studied the relation between bisimulation and symmetry groups of the dynamics. We also provided a game interpretation for two of the behavioural equivalences. The present work unifies the cited conference presentations and gives detailed proofs.
Publisher
Cambridge University Press (CUP)
Subject
Computer Science Applications,Mathematics (miscellaneous)
Reference28 articles.
1. Pachl, J. and Terraf, P. S. (2020). Semipullbacks of labelled Markov processes. ArXiv e-prints, 1706.02801. To be published in Logical Methods in Computer Science.
2. Bisimulation for labelled Markov processes
3. Handbook of Brownian motion-facts and formulae;Borodin;Journal of the Royal Statistical Society-Series A Statistics in Society,1997
4. Labelled Markov Processes
5. Bisimulation and cocongruence for probabilistic systems