Expressiveness of Probabilistic π-calculus

In this work we propose a probabilistic extension of the π-calculus. The main novelty is a probabilistic mixed choice operator, that is, a choice construct with a probability distribution on the branches, and where input and output actions can both occur as guards. We develop the operational semantics of this calculus, and then we investigate its expressiveness. In particular, we compare it with the sublanguage with the two separate choices, where input and output guards are not allowed together in the same choice construct. Our main result is that the separate choices can encode the mixed one. Further, we show that input-guarded choice can encode output-guarded choice and viceversa. In contrast, we conjecture that neither of them can encode the pair of the two separate choices.