On the Semantic Foundations of Probabilistic Synchronous Reactive Programs

In this paper we consider synchronous parallel programs P that are composed by sequential randomized processes S Sk which communicate via shared variables First we give an operational semantics for the sequential components Si on the basis of a transition relation de ned in the classical SOS style a la Plotkin Plo which we use to specify the behaviour of P by a Markov chain whose transitions stand for the cumulative e ect of the activities of the components S Sk within one time step Second we provide a denotational semantics for P that also models P by a Markov chain It is based on a denotational least xed point semantics for the sequential components which formalizes the input output behaviour of the sequential components within one time step While the operational declarative semantics might be the one that a designer who provides the input for the tool has in mind the denotational procedural semantics is the one that a compiler might use We establish a consistency result stating that the Markov chains induced by the operational and denotational semantics are bisimilar in the sense of LS