On the Problem of Computing the Probability of Regular Sets of Trees

Henryk Michalewski (1) , Matteo Mio (2, 3)

1 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
2 ENS de Lyon - École normale supérieure de Lyon
3 PLUME - Preuves et Langages

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 examples three properties of measure: (1) there exist regular sets having irrational probability, (2) there exist comeager regular sets having probability 0 and (3) the probability of game languages W i,k , from automata theory, is 0 if k is odd and is 1 otherwise.

Mots clés: Models of Computation; regular languages of trees; probability; meta-parity games

Domaines: Logique en informatique [cs.LO]

Henryk Michalewski, Matteo Mio. On the Problem of Computing the Probability of Regular Sets of Trees. Proc. of FSTTCS 2015, Dec 2015, Bangalore, India. pp.489 - 502, ⟨10.4230/LIPIcs.FSTTCS.2015.489⟩. ⟨hal-02140487⟩