Question

Given an NFA N, prove that there exists an NFA N' with one accept state that...

Given an NFA N, prove that there exists an NFA N' with one accept state that recognizes the same language as N.

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Answer #1

Any NFA can be converted into a new NFA with only one final state that accepts the same language.

This can be done with the help of epsilon transitions.

Simply create a new final state and connect all the previous final states to it with epsilon transitions.

All the older final states would be regular states now. An example of this is shown in the image.

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