Equivalence of Probabilistic \(\mu \)-Calculus and p-Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


An important characteristic of Kozen’s \(\mu \)-calculus is its strong connection with parity alternating tree automata. Here, we show that the probabilistic \(\mu \)-calculus \(\mu ^p\)-calculus and p-automata (parity alternating Markov chain automata) have an equally strong connection. Namely, for every \(\mu ^p\)-calculus formula we can construct a p-automaton that accepts exactly those Markov chains that satisfy the formula. For every p-automaton we can construct a \(\mu ^p\)-calculus formula satisfied in exactly those Markov chains that are accepted by the automaton. The translation in one direction relies on a normal form of the calculus and in the other direction on the usage of vectorial \(\mu ^p\)-calculus. The proofs use the game semantics of \(\mu ^p\)-calculus and automata to show that our translations are correct.




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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of LeicesterLeicesterUK

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