Results on homomorphic realization of automata by α0-products

Abstract

AbstractThe notion of an irreducible semigroup has been fundamental to the Krohn-Rhodes decomposition. In this paper we study a similar concept and point out its equivalence with the Krohn-Rhodes irreducibility. We then use the new aspect of irreducible semigroups to provide cascade decompositions of automata in a situation when a strict letter-to-letter replacement is essential. The results are stated in terms of completeness theorems. Our terminology follows Gécseg (1986), so that the cascade composition is referred to as the α0-product