Algorithmic bisimulation for Communicating Piecewise Deterministic Markov Processes

Abstract

Abstract-In this paper we present an algorithm for finding a bisimulation relation for stochastic hybrid systems from the class of CPDPs (Communicating Piecewise Deterministic Markov Processes). We prove that the fixed point of the algorithm forms a bisimulation on the state space of the CPDP. We give sufficient conditions on the continuous dynamics and the transition structure of a CPDP, for the computation of the algorithm to be decidable.

Approximations of Stochastic Hybrid Systems

“…The infinitesimal generator of the process is given in [15], [29] as (23) assuming that is in the domain of the generator. The following theorem gives a sufficient condition for the construction of a stochastic simulation function of by .…”

“…Approximate bisimulation naturally generalize exact notions of system refinement and equivalence [20], [21]. Notions of exact bisimulation have been recently developed for some classes of stochastic hybrid systems in [22], [23]. In particular, in [22], a notion of exact bisimulation for general stochastic hybrid systems is developed using notions from category theory, whereas in [23] the issue of exact bisimulation is treated for the so called communicating piecewise deterministic hybrid systems.…”

HYPE with stochastic events

“…The synchronization mechanics of CPDP has been extended in [14], introducing an operator which exploits all possible interactions of active and passive actions. In [15] the authors define a notion of bisimulation for both PDMPs and CPDPs and show that if CPDPs are bisimilar then they give rise to bisimilar PDMPs. Furthermore the equivalence relation is a congruence with respect to the composition operator of CPDPs.…”

Compositional Modelling of Stochastic Hybrid Systems

“…We investigate for which scheduled CPDPs such a composition 'makes sense', and for those scheduled CPDPs we define the composition such that the class of scheduled CPDPs is closed under this composition. This chapter is based on [SvdS05d,SvdS05a] Chapter 9 In this chapter we define bisimulation for CPDPs and for scheduled CPDPs. We show that the substitutivity property holds and we show that under maximal progress, bisimilar scheduled CPDPs have the same stochastic behavior.…”

“…For a restricted class of CPDPs we give an algorithm that automatically computes bisimulation relations for CPDPs and scheduled CPDPs. This chapter is based on [SvdS05c,SvdS05a].…”