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I have a NFA like this:

enter image description here

and the question is:

Are epsilon and empty set languages of this NFA?

Mat
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Lucas
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  • Is that a Σ or an ε? – Josh Lee Jun 24 '17 at 14:08
  • You're asking if the NFA accepts the empty word? – C-Otto Jun 24 '17 at 14:08
  • At the picture it is a Σ. @C-Otto I know it doesnt, but the question is a bit tricky : / Because Σ and empty set are, by definition, languages over every Σ. – Lucas Jun 24 '17 at 14:09
  • I don't understand your question. Could you provide more information, add some examples of cases related to your question? – C-Otto Jun 24 '17 at 14:11
  • @C-Otto, the thing is, I dont have any more informations :D The question is from an exam, and it says nothin more. The exact question is: "Both, empty set and epsilon, are, by definition, language over every alphabet; are they languages of this NFA? (by THIS I mean the NFA from the image above). OUH, one more thing - Σ = {a,b,c,d} – Lucas Jun 24 '17 at 14:14
  • I think I would reword that to: "Does this NFA accept the empty string? Does this NFA accept no strings at all?" – Josh Lee Jun 24 '17 at 14:16
  • @JoshLee, it doesnt ;d But are you sure it is correct reword? – Lucas Jun 24 '17 at 14:17

1 Answers1

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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.

Mat
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  • Thank you Mat :) Can I ask one more question? How would you transform this NFA to DFA? – Lucas Jun 24 '17 at 17:48
  • @Lucas You're welcome. Sadly I that is out of the scope of your question, if you have difficulties with the steps, I'd suggest you go read [This fairly good example](https://www.tutorialspoint.com/automata_theory/ndfa_to_dfa_conversion.htm). If you still do not succeed, you may post another question. – Mat Jun 24 '17 at 17:58