## Sylvain Lombardy ; Jacques Sakarovitch - Morphisms and minimisation of weighted automata

fi:8870 - Fundamenta Informaticae, October 21, 2022, Volume 186, Issues 1-4: Trakhtenbrot's centenary
Morphisms and minimisation of weighted automata

Authors: Sylvain Lombardy ; Jacques Sakarovitch

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.

Volume: Volume 186, Issues 1-4: Trakhtenbrot's centenary
Published on: October 21, 2022
Accepted on: July 7, 2022
Submitted on: December 20, 2021
Keywords: Computer Science - Discrete Mathematics,Computer Science - Formal Languages and Automata Theory