On the structure of finite automata of whichM′ is an (weak) inverse with delay τ

In this paper, we first give a method that for any inverse finite automaton M′ with delay τ, all inver tible finite automata with delay τ, of whichM′ is an inverse with delay τ, can be constructed; and a universal nondeterministic finite automaton, for all finite automata of whichM′ is an inverse with delay τ, can also be constructed. We then give a method that for any weak inverse finite automatonM′ with delay τ, all weakly invertible finite automata with delay τ of whichM′ is a weak inverse with delay, can be constructed; and a universal nondeterministic finite automaton, for all finite automata of whichM′ is a weak inverse with delay τ, can also be constructed.