Dynamic Logic of Communicating Hybrid Programs

Abstract

This paper presents a dynamic logic $d{\mathcal{L}}_{\text{CHP}}$ for compositional deductive verification of communicating hybrid programs (CHPs). CHPs go beyond the traditional mixed discrete and continuous dynamics of hybrid systems by adding CSP-style operators for communication and parallelism. A compositional proof calculus is presented that modularly verifies CHPs including their parallel compositions from proofs of their subprograms by assumption-commitment reasoning in dynamic logic. Unlike Hoare-style assumption-commitments, $d{\mathcal{L}}_{\text{CHP}}$ supports intuitive symbolic execution via explicit recorder variables for communication primitives. Since $d{\mathcal{L}}_{\text{CHP}}$ is a conservative extension of differential dynamic logic $d\mathcal{L}$, it can be used soundly along with the $d\mathcal{L}$ proof calculus and $d\mathcal{L}$'s complete axiomatization for differential equation invariants.