Autómatas ponderados sobre bimonoides fuertes

Abstract

Weighted automata make it possible to obtain information by assigning weights to transitions in the automata, through semantics. These weights can represent different types of information, such as the amount of resources necessary to execute a transition or the probability of its successful execution. The semantic interpretation may vary depending on the algebraic structure with which that is associated. Although the literature on weighted automata focuses mainly on semirings, the article mainly argues why the algebraic structure associated with an automaton must meet the minimum requirement of being a strong bimonoid, even if the half ring is perceived as more optimal. In addition, mathematical tools are presented, such as recognizable functions, which allow characterize automata through various languages and approach the study of bimonoids locally through finite subsets. The theory generated enables us to use mathematics and science computational in establishing relationships between the different semantics associated with auto- recognizable bushes. Also, it allows us to explore varied interpretations, recognizable functions, and local finite properties of bimonoids.