Structure of weakly invertible semi-input-memory finite automata with delay 1

Abstract

Semi-imput-memory finite automata, a kind of finite automata introduced by the first author of this paper for studying error propagation, are a generalization of inputmemory finite automata by appending an autonomous finite automaton component. In this paper, we give a characterization of the structure of weakly invertible semi-input-memory finite automata with delay 1, in which the state graph of each autonomous finite automaton is a cycle. From a result on mutual invertibility of finite automata obtained by the authors recently, it leads to a characterization of the structure of feedforward inverse finite automata with delay 1.