Equivalence of Probabilistic $$\mu $$ -Calculus and p-Automata [chapter]

Claudia Cauli, Nir Piterman
2017 Lecture Notes in Computer Science  
An important characteristic of Kozen's µ-calculus is its strong connection with parity alternating tree automata. Here, we show that the probabilistic µ-calculus µ p -calculus and p-automata (parity alternating Markov chain automata) have an equally strong connection. Namely, for every µ 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 µ p -calculus formula satisfied in exactly those
more » ... kov 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 µ p -calculus. The proofs use the game semantics of µ p -calculus and automata to show that our translations are correct.
doi:10.1007/978-3-319-60134-2_6 fatcat:4wp4flajcnhq7ohyy7ywdq3qxa