Extending Hybrid CSP with Probability and Stochasticity

Abstract

Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly intertwining discrete, continuous and stochastic dynamics complicates modelling, analysis and verification of stochastic hybrid systems SHSs. In the literature, this issue has been extensively investigated, but unfortunately it still remains challenging as no promising general solutions are available yet. In this paper, we give our effort by proposing a general compositional approach for modelling and verification of SHSs. First, we extend Hybrid CSP HCSP, a very expressive and process algebra-like formal modeling language for hybrid systems, by introducing probability and stochasticity to model SHSs, which is called stochastic HCSP SHCSP. To this end, ordinary differential equations ODEs are generalized by stochastic differential equations SDEs and non-deterministic choice is replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic HHL to specify and reason about SHCSP processes. We demonstrate our approach by an example from real-world.