Reasoning about efficiency within a probabilistic µ-calculus

Expectation-based probabilistic predicate transformers 15] provide a logic for probabilistic sequential programs, giving access to expressions such as`the probability that predicate A is achieved nally'. Using expectations more generally however, we can express-calculus formulae for the expected path-length of a computation tree. Moreover within an expectation-based-calculus such eeciency measures and more conventional (but probabilistic) temporal operators 14] can be related.