Structure of Weakly Invertible Semi-Input-Memory Finite Automata with Delay 1

Semi-input-memory finite automata, a kind of finite automata introducedby the first author of this paper for studying error propagation, are ageneralization of input-memory finite automata by appending an autonomousfinite automaton component.In this paper, we give a characterization of the structure of weaklyinvertible semi-input-memory finite automata with delay 1, in whichthe state graph of each autonomous finite automaton is a cycle.From a result on mutual invertibility of finite automata obtained bythe authors recently, it leads to a characterization of the structureof feedforward inverse finite automata with delay 1.