Bisimulation for communicating piecewise deterministic markov processes (CPDPs)

Authors:
Stefan Strubbe;Arjan van der Schaft
Affiliations:
Twente University, Enschede, The Netherlands;Twente University, Enschede, The Netherlands
Venue:
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Year:
2005

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Abstract

CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition. Then we introduce a notion of bisimulation for PDPs and CPDPs and we prove that bisimilar PDPs as well as bisimilar CPDPs have equal stochastic behavior. Finally, as main result, we prove the congruence property that, for a composite CPDP, substituting components by different but bisimilar components results in a CPDP that is bisimilar to the original composite CPDP (and therefore has equal stochastic behavior).