Retractable state-finite automata without outputs

Abstract

A homomorphism of an automaton A without outputs onto a subautomaton B of A is called a retract homomorphism if it leaves the elements of B fixed. An automaton A is called a retractable automaton if, for every subautomaton B of A, there is a retract homomorphism of A onto B. In [1] and [3], special retractable automata are examined. The purpose of this paper is to give a construction for state-finite retractable automata without outputs.