Automata over MV-algebras [many-valued logic]

We propose the notion of automata over Lukasiewicz many-valued logic, extending fuzzy automata (E. Santos, Info. and Control, vol.13, p.363-377, 1968). Indeed, W-algebras, i.e., algebraic structures related with many-valued Lukasiewicz logic, are made of two semiring reducts obtained considering the supremum operation together with the Lukasiewicz conjunction and the infimum operation together with Lukasiewicz disjunction. Vice-versa, given two semirings over the same domain, and given an isomorphism between these two algebras, we can set some conditions in order to have an MV-algebra. Following the tradition of semirings, in this paper, we study "many-valued automata" and "many-valued formal languages" interpreted in Lukasiewicz logic.