Linear realization of finite automata

摘要

This paper presents a method for linear realization of automata when such exists.The basic tools employed are indexed partitions (as a way of writing certain mappings) and predecessor operations. The indexed partitions are studied in some detail and their connection to codes is explained. The method itself is simple and straightforward and contains no search steps. Only standard techniques of linear algebra, such as solving linear equations, are used. Examples are given to show the advantage of our method compared with previously known ones.