The Rees Matrix Reduction of the Input Semigroup of a Finite Strongly Connected Automaton

摘要

In the paper it is proposed to reduce essentially the study of finite, strongly connected automata to the study of the same type of automata over certain Rees matrix semigroups. In the process the automorphism groups of the former are determined; specifically the study of all such automata is thereby recast into problems of the theory of finite groups. (Author)