Two Routes to Automata Minimization and the Ways to Reach It Efficiently

Sylvain Lombardy (1) , Jacques Sakarovitch (2, 3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
3 CNRS - Centre National de la Recherche Scientifique

This paper reports on the work done for the implementation of the algorithms for the computation of the minimal quotient of an automaton in the Awali platform. In the case of non-deterministic or of weighted automata, the minimal quotient of an automaton is obtained by merging all states in bisimulation. Two strategies are explored for the computation of the coarsest bisimulation equivalence. The first one is an extension of the Moore algorithm for the computation of the minimal quotient of a DFA; the second one is inspired by the Hopcroft algorithm for the same problem. These two strategies yield algorithms with the same quadratic complexity and we study the cases where the second strategy can be improved in order to achieve a complexity similar to the one of Hopcroft algorithm.

Mots clés: Weighted automata; Minimization; Bisimulation

Domaines: Théorie et langage formel [cs.FL]

Sylvain Lombardy, Jacques Sakarovitch. Two Routes to Automata Minimization and the Ways to Reach It Efficiently. International Conference on Implementation and Application of Automata, CIAA 2018, Jul 2018, Charlottetown, Canada. pp.248-260, ⟨10.1007/978-3-319-94812-6_21⟩. ⟨hal-01866176⟩