Towards a Classification of Behavioural Equivalences in Continuous-time Markov Processes

Chen, Linan; Clerc, Florence; Panangaden, Prakash

doi:10.1016/j.entcs.2020.09.004

Cited by 1 publication

(5 citation statements)

References 30 publications

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“…We later came up with other notions of behavioural equivalences, and in Chen et al (2020), we proposed three other notions of behavioural equivalences. It is quite likely that there are other interesting notions to be studied in future works.…”

Section: Temporal Equivalencementioning

confidence: 99%

“…An interesting notion that appears when looking at examples is that of symmetries of a system. It was the third notion introduced in Chen et al (2020).…”

Section: Symmetries Of Systemsmentioning

confidence: 99%

“…This is an example that we considered in Chen et al (2020). A Poisson process models a continuous-time process in which a discrete variable is incremented.…”

Section: Poisson Processmentioning

confidence: 99%

“…We have adapted that game to the continuous-time setting. We have published those games in Chen et al (2020). We will omit the proofs in this section but they can be found in Clerc (2021).…”

Section: Definition Of Cospansmentioning

confidence: 99%

“…We have published those games in Chen et al (2020). We will omit the proofs in this section but they can be found in Clerc (2021). However, it is especially interesting to note that the game interpretation of bisimulation emphasises once again the role of trajectories in that concept whereas the game interpretation of temporal equivalence resembles that in discrete time very closely.…”

Section: Definition Of Cospansmentioning

confidence: 99%

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Behavioural equivalences for continuous-time Markov processes

Chen

Clerc

Panangaden

2023

Math. Struct. Comp. Sci.

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Bisimulation 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.

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Section: Temporal Equivalencementioning

confidence: 99%

“…An interesting notion that appears when looking at examples is that of symmetries of a system. It was the third notion introduced in Chen et al (2020).…”

Section: Symmetries Of Systemsmentioning

confidence: 99%

“…This is an example that we considered in Chen et al (2020). A Poisson process models a continuous-time process in which a discrete variable is incremented.…”

Section: Poisson Processmentioning

confidence: 99%

Section: Definition Of Cospansmentioning

confidence: 99%

Section: Definition Of Cospansmentioning

confidence: 99%

See 3 more Smart Citations