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.

翻译：本文研究加权自动数据最小化的算法。 它从形态学定义开始, 它概括并统一了对整类加权自动数据进行平衡的概念, 以及每个自动图的最小商数的单一性, 这是通过分区精细获得的 。 从精细分区的一般方法来看, 在计算最小商数时, 考虑了两种策略: 域分割法和先行分类法。 它们与古典摩尔法和Hopcroft 算法相对应, 用于计算确定性布洛兰自动数据最低商数。 我们显示, 这两种策略产生具有相同二次复杂度的算法, 当第二个算法可以改进, 以便实现与霍克罗夫特算法相似的复杂度时, 我们研究这些案例 。