Qualitative Tree Languages

Arnaud Carayol (1) , Axel Haddad (1, 2) , Olivier Serre (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We study finite automata running over infinite binary trees and we relax the notion of accepting run by allowing a negligible set (in the sense of measure theory) of non-accepting branches. In this qualitative setting, a tree is accepted by the automaton if there exists a run over this tree in which almost every branch is accepting. This leads to a new class of tree languages, called the qualitative tree languages that enjoys many properties. Then, we replace the existential quantification --a tree is accepted if there exists some accepting run over the input tree-- by a probabilistic quantification --a tree is accepted if almost every run over the input tree is accepting. Together with the qualitative acceptance and the Büchi condition, we obtain a class of probabilistic tree automata with a decidable emptiness problem. To our knowledge, this is the first positive result for a class of probabilistic automaton over infinite trees.

Mots clés: Tree Automata; Probabilistic Automata; Markov Decision Process

Domaines: Informatique et langage [cs.CL]

Arnaud Carayol, Axel Haddad, Olivier Serre. Qualitative Tree Languages. Twenty-Sixth Annual IEEE Symposium on Logic in Computer Science (LICS 2011), 2011, Toronto, Canada. pp.13-22, ⟨10.1109/LICS.2011.28⟩. ⟨hal-00616304⟩