A Class of Probabilistic Automata with a Decidable Value 1 Problem

Nathanaël Fijalkow (1, 2) , Hugo Gimbert (3) , Youssouf Oualhadj (3)

1 ENS Cachan - École normale supérieure - Cachan
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton, are there words accepted with probability arbitrarily close to 1? This problem was proved undecidable recently. We introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is decidable. The algorithm is based on the computation of a monoid abstracting the behaviors of the automaton. The correctness proof relies on algebraic techniques developped by Simon.

Mots clés: Probabilistic automata; value 1 problem

Domaines: Informatique et théorie des jeux [cs.GT]; Théorie et langage formel [cs.FL]

Nathanaël Fijalkow, Hugo Gimbert, Youssouf Oualhadj. A Class of Probabilistic Automata with a Decidable Value 1 Problem. 2011. ⟨hal-00585835v1⟩