Towards automated proof support for probabilistic distributed systems

Abstract. The mechanisation of proofs for probabilistic systems is particularly challenging due to the verification of real-valued properties that probability entails: experience indicates [12, 4, 11] that there are many difficulties in automating real-number arithmetic in the context of other program features. In this paper we propose a framework for verification of probabilistic distributed systems based on the generalisation of Kleene algebra with tests that has been used as a basis for development of concurrency control in standard programming [7]. We show that verification of real-valued properties in these systems can be considerably simplified, and moreover that there is an interpretation which is susceptible to counterexample search via state exploration, despite the underlying real-number domain.