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I have a doubt regarding NFA

Consider 

So this NFA will accept strings like b,ab. But what if a string aba comes? Will it be accepted? The question I have is that with 'ab' it will be in the final state and with 'a' as in input, with no transition defined it will still be in final state? So technically it should be accepted right?

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for NFA only important moves are mentioned . if you find NFA with lacking some input i mean if there is no transition mentioned for some input then that's mean this input is not important. Technically this input may lead to Dead state so above NFA contains L ={a*b}. for state Q if no further transition is mentioned then they are actually leading to dead state. its basic concept.

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