On the Structure of Finite Automata of Which M'Is an(Weak)Inverse with Delay τ

In this paper,we first give a method that for any inverse finite automaton M’ withdelay τ,all inver tible finite automata with delay τ,of which M’ is an inverse with delayτ,can be constructed;and a universal nondeterministic finite automaton,for all finiteautomata of which M’ is an inverse with delay τ,can also be constructed.We then give amethod that for any weak inverse finite automaton M’ with delay τ,all weaklyinvertible finite automata with delay τ of which M’ is a weak inverse with delay,can beconstructed;and a universal nondeterministic finite automaton,for all finiteautomata of which M’ is a weak inverse with delay τ,can also be constructed.