Probabilistic Automata of Bounded Ambiguity

Nathanaël Fijalkow (1, 2) , Cristian Riveros (3) , James Worrell (4)

1 CNRS - Centre National de la Recherche Scientifique
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 UC - Pontificia Universidad Católica de Chile
4 Department of Computer Science [Oxford]

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are undecidable. In this work we focus on the emptiness problem (and its variant the value problem), which asks whether a given probabilistic automaton accepts some word with probability greater than a given threshold. We consider a natural and well-studied structural restriction on automata, namely the degree of ambiguity, which is defined as the maximum number of accepting runs over all words. The known undecidability proofs exploits infinite ambiguity and so we focus on the case of finitely ambiguous probabilistic automata. Our main contributions are to construct efficient algorithms for analysing finitely ambiguous probabilistic automata through a reduction to a multi-objective optimisation problem called the stochastic path problem. We obtain a polynomial time algorithm for approximating the value of probabilistic automata of fixed ambiguity and a quasi-polynomial time algorithm for the emptiness problem for 2-ambiguous probabilistic automata. We complement these positive results by an inapproximability result stating that the value of finitely ambiguous probabilistic automata cannot be approximated unless P = NP.

Mots clés: probabilistic automata; weighted automata; multi-objective optimisation

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

Nathanaël Fijalkow, Cristian Riveros, James Worrell. Probabilistic Automata of Bounded Ambiguity. Information and Computation, In press. ⟨hal-02503353⟩