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automatanon-deterministic

Is epsilon and empty set languages of NFA? (Nondeterministic Finite Automata)

I have a NFA like this:

enter image description here

and the question is:

Are epsilon and empty set languages of this NFA?

Solution

  • Your automata needs a minimum of {b,a} in order to reach its end state. Therefore, since it's impossible to reach the end with no transition, empty set isn't in its language. Also since there isnt a path from start to finish that is composed entirely of ε-transitions, there's no way to reach the end state with only ε.

    So no, Empty set and ε are Not part of that NFA's languages.