(T/F) Given an NFA that has null/epsilon transitions, one can create another NFA that accepts the same language but has NO null-transitions

Question

True or false and say why:

Given an NFA that has null/epsilon transitions, one can create another NFA that accepts the same language but has NO null-transitions.

True, there is an algorithm for this: https://cs.stackexchange.com/questions/16237/removing-null-moves-from-nfa — Welbog, Sep 19 '19 at 13:39

score 1 · Answer 1 · answered Oct 14 '19 at 15:20

This is true. The idea is that for every state, you find the set of states reachable from it by traversing only null/epsilon transitions. Then, you update all transitions that terminate in that state to terminate in the set of reachable states. At that point, it's safe to remove the null/epsilon transitions.

Depending on what you're allowed to rely on, you could simply argue that a NFA with null/epsilon transitions describes a regular language, and regular languages have DFAs, and DFAs are NFAs without null/epsilon transitions.

(T/F) Given an NFA that has null/epsilon transitions, one can create another NFA that accepts the same language but has NO null-transitions

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