SOME PROPERTIES ON THE STRUCTURE OF INVERTIBLE AND INVERSE FINITE AUTOMATA WITH DELAY τ

Given a finite automaton M=X, Y, S, δ, λith Card(X)=Card(Y), M. being invertible with delay T. A universal inverse finite automaton of M with delay τ can be constructed, of which the set of all subautomata with the input alphabet Y, the output alphabet X and a nonempty state alphabet is a distributive lattice with a greatest element and least element and is equal to the set of all inverse finite automata of M with delay T up to equivalence.Given a finite automaton M' =Y, X, S', δ', λ',ith Card(X)=Card(Y). M' being an inverse with delay T of some invertible finite automaton with delay $. A universal invertible finite automaton with delay T relating to M' can be constructed, of which the set of all subautomata with the input alphabet X, the output alphabet Y and anon-empty state alphabet is a distributive lattice with a greatest element and a least element and is equal up to equivalence to the set of all finite automata of which M' is an inverse with delay τ.