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I am studying Theory of Automata. I was studying conversion of Epsilon-NFA to NFA. I had to take null closures of states two times, before and after the specific input.

Could someone explain, what is the reason behind this?

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You might need to do some $\varepsilon$-transitions before reading the first character of the input, and after reading the last character. It's probably easier to just consider them before and after every character, so every character is treated the same way, than to make a special case of the first or last character.

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