Structural Preserving Morphisms of Finite Automata and an Application to Graph Isomorphism

The transition preserving morphisms (endomorphism, homomorphism, isomorphism, and automorphism) of state machines are developed on the basis of nontrivial closed partitions over their state sets. Algorithms with illustrated examples are provided for determining these morphisms. By means of these morphisms, the structural preserving morphisms of finite automata can be readily solved by simply making a constraint on each partition being not only nontrivial and closed but also output-consistent.