Probabilistic Mu-Calculus: Decidability and Complete Axiomatization

Authors Kim G. Larsen, Radu Mardare, Bingtian Xue

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Kim G. Larsen
Radu Mardare
Bingtian Xue

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Kim G. Larsen, Radu Mardare, and Bingtian Xue. Probabilistic Mu-Calculus: Decidability and Complete Axiomatization. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We introduce a version of the probabilistic mu-calculus (PMC) built on top of a probabilistic modal logic that allows encoding n-ary inequational conditions on transition probabilities. PMC extends previously studied calculi and we prove that, despite its expressiveness, it enjoys a series of good meta-properties. Firstly, we prove the decidability of satisfiability checking by establishing the small model property. An algorithm for deciding the satisfiability problem is developed. As a second major result, we provide a complete axiomatization for the alternation-free fragment of PMC. The completeness proof is innovative in many aspects combining various techniques from topology and model theory.
  • Markov process
  • probabilistic modal mu-calculus
  • n-ary (in-)equational modalities
  • satisfiability
  • axiomatization


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