Simplification of Intermediate Results during Intersection of Multiple Weighted Automata

This paper presents a new simplification method for weighted finite automata. The method suggests efficient approaches to some problems that are related to intersection of automata. Minimal automata can be made smaller through simplifications such as merging of states. Although such simplifications change the recognized language, some other essential properties of the automaton may be preserved. For example, if we want to count, in a deterministic automaton, the strings whose length is below some limit, we can first merge some states and then count the number of strings using the simplified result that may be smaller than a minimal automaton [3]. The idea of various simplifications that preserve certain essential properties lends itself also to the case where the strings are described conjuctively, by an intersection of multiple automata. State merging when computing properties of an intersection can reduce the overal time complexity, and it resembles the projection operation of relation tables that is used in query optimization in modern database systems [5]. Our method assumes that an intersection of multiple minimal automata is carried out through pairwise intersections of automata. Some properties in the automata to be intersected indicate redundancy that leads to simple optimizations that are possible especially in unweighted automata, but also in some classes of weighted automata: