In this paper we work on (bi)simulation semantics of processes that exhibit
both nondeterministic and probabilistic behaviour. We propose a probabilistic
extension of the modal mu-calculus and show how to derive characteristic
formulae for various simulation-like preorders over finite-state processes
without divergence. In addition, we show that even without the fixpoint
operators this probabilistic mu-calculus can be used to characterise these
behavioural relations in the sense that two states are equivalent if and only
if they satisfy the same set of formulae.Comment: 18 page