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The probabilistic (or quantitative) modal µ-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every process state a value in the interval [0, 1] representing the probability that the property expressed by the formula holds(More)
The probabilistic modal µ-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS's). Two equivalent semantics have been studied for this logic, both assigning to each state a value in the interval [0, 1] representing the probability that the property expressed by the formula holds at the state.(More)
We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by game automata. In particular this algorithm is applicable to all deterministic automata. We then use the algorithm to prove through(More)
We present a formal proof system for compositional verification of probabilistic concurrent processes. Processes are specified using an SOS-style process algebra with probabilistic operators. Properties are expressed using a probabilistic modal µ-calculus. And the proof system is formulated as a sequent calculus in which sequents are given a quantitative(More)