How do I convert the following GNFA to regular expression?

Question

Here is a GNFA I made from an NFA.

I'm unsure how to treat the node of b(a∪b)* (the first node after the start node and the one below it). Since it doesn't lead to any goal state, do I disregard it in when I generate the regular expression?

Short answer: Yes, you can delete this state for the reason you mentioned. For more information have a look at this Community question: How to convert finite automaton to regular expression — ttnick, Oct 15 '18 at 21:05

score 1 · Answer 1 · answered Oct 16 '18 at 01:41

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Given an NFA, we can simplify it to an equivalent NFA with possibly fewer states by repeatedly applying the following two pruning steps:

Remove any states which are not reachable from the initial state.
Remove any states from which no final state can be reached.

In your case, this will result in removing the left bottom state.

answered Oct 16 '18 at 01:41

Yuval Filmus

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As an aside, one way this is often implemented in software when constructing DFAs is to add a known null state (i.e. a state which is not reachable from the initial state), performing DFA minimisation, and then removing any states which end up in the same class as that known null state. – Pseudonym Apr 08 '20 at 06:33

How do I convert the following GNFA to regular expression?

1 Answers1