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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 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)

- Ernst W Mayr, Nicolas Ollinger, Susanne Albers, Tu München, Chris Hankin, Michael Mitzenmacher +494 others
- 2015

In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors' moral rights: Attribution: The work must be attributed to its authors. LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIcs… (More)

- Matteo Mio
- 2010

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)

The paper explores properties of Łukasiewicz µ-calculus, a version of the quantitative/probabilistic modal µ-calculus containing both weak and strong conjunctions and disjunctions from Łukasiewicz (fuzzy) logic. We show that this logic encodes the well-known probabilistic temporal logic PCTL. And we give a model-checking algorithm for computing the rational… (More)