Behavioural equivalences of a probabilistic pi-calculus

Abstract

Although different kinds of probabilistic π-calculus have been introduced and found their place in quantitative verification and evaluation, their behavioural equivalences still lack a deep investigation. We propose a simple probabilistic extension of the π-calculus, πp, which is inspired by Herescu and Palamidessi’s probabilistic asynchronous π-calculus. An early semantics of our πp is presented. We generalise several classic behavioural equivalences to probabilistic versions, obtaining the probabilistic (strong) barbed equivalence and probabilistic bisimulation for πp. Then we prove that the coincidence between the barbed equivalence and bisimilarity in the π-calculus is preserved in the probabilistic setting.