Morphisms and Minimisation of Weighted Automata

Issue title: Special Issue of Invited Papers in Honor of the Boris Trakhtenbrot Centenary

Guest editors: Arnon Avron, Nachum Dershowitz and Alexander Rabinovich

Article type: Research Article

Authors: Lombardy, Sylvain^a | Sakarovitch, Jacques^{b; *}

Affiliations: [a] LaBRI - UMR 5800 - Bordeaux INP - Bordeaux University - CNRS, Bordeaux, France. Sylvain.Lombardy@labri.fr | [b] IRIF - CNRS/Paris Cité University and Telecom Paris, IPP, Paris, France. sakarovitch@enst.fr

Correspondence: [*] Address for correspondence: IRIF - CNRS/Paris Cité University and Telecom Paris, IPP.

Abstract: This paper studies the algorithms for the minimisation of weighted automata. It starts with the definition of morphisms — which generalises and unifies the notion of bisimulation to the whole class of weighted automata — and the unicity of a minimal quotient for every automaton, obtained by partition refinement. From a general scheme for the refinement of partitions, two strategies are considered for the computation of the minimal quotient: the Domain Split and the Predecesor Class Split algorithms. They correspond respectivly to the classical Moore and Hopcroft algorithms for the computation of the minimal quotient of deterministic Boolean automata. We show that these two strategies yield algorithms with the same quadratic complexity and we study the cases when the second one can be improved in order to achieve a complexity similar to the one of Hopcroft algorithm.

DOI: 10.3233/FI-222126

Journal: Fundamenta Informaticae, vol. 186, no. 1-4, pp. 195-218, 2022