Algorithm of Learning Weighted Automata

Weighted automata is a quantitative formalism of finite automata, where for each transition there adheres a weight, and the domain of all weights is a Semiring. The existing learning algorithms for weighted automata assume the domain of weights being a Field. In this paper, we prove the learnability of weighted automata from Field to LC - Semiring, a special case of Semiring satisfying the linear combination property. A new algorithm based on the exact learning model is proposed. The experimental results on a collection of examples confirm that the space advantage of our learning algorithm for deterministic and weighted automata.