What is known about the Value 1 Problem for Probabilistic Automata?

Nathanaël Fijalkow (1, 2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

The value 1 problem is a decision problem for probabilistic automata over finite words: are there words accepted by the automaton with arbitrarily high probability? Although undecidable, this problem attracted a lot of attention over the last few years. The aim of this paper is to review and relate the results pertaining to the value 1 problem. In particular, several algorithms have been proposed to partially solve this problem. We show the relations between them, leading to the following conclusion: the Markov Monoid Algorithm is the most correct algorithm known to (partially) solve the value 1 problem.

Mots clés: Probabillistic Automata; Value 1 Problem

Domaines: Informatique et théorie des jeux [cs.GT]

Nathanaël Fijalkow. What is known about the Value 1 Problem for Probabilistic Automata?. 2014. ⟨hal-01074111⟩