Extended Nondeterministic Finite Automata

We consider a new expansion of nondeterministic finite automata. The goals of this consideration are: to apply some algorithms of such expansion for various problems of minimization of classical nondeterministic automata; to use such automata for describing practical anytime algorithms for the same problems of minimization; using such automata, we often can simplify some proofs for algorithms of simplification of usual nondeterministic automata.