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

  • Claudia Cauli
  • Nir Piterman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)

Abstract

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.

Keywords

Markov Chain Atomic Proposition Tree Automaton Modal Formula Semantic Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of LeicesterLeicesterUK

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