Conversion of nfa with self-loop to one without self-loop For every nondeterministic finite state automata that has self-loop(s), there exists an equivalent nfa that does not have any self-loop. How can we prove this statement in a general basis without the use of examples?
Add a new state and make the self loop point to the new state and add a empty transition from the new state back to the original state.

It is straightforward to prove that this NFA is equivalent to the original.