Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

TL;DR

This paper explores bisimulation relations among automata, stochastic differential equations, and Petri nets, enabling combined formal verification and analysis capabilities for complex stochastic systems.

Contribution

It introduces bisimilarity relations between stochastic hybrid automata, stochastic differential equations, and Petri nets, facilitating their integration for system analysis.

Findings

Bisimilarity relations are established between the models.

Combined formal verification and analysis methods are demonstrated.

An air traffic example illustrates the practical application.

Abstract

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.