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Suppose a regular language L is closed under the operation halving, then the result would be:

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Suppose a regular language L is closed under the operation halving, then the result would be:

(a) 1/4 L will be regular

(b) 1/2 L will be regular

(c) 1/8 L will be regular

(d) Al of the mentioned

This question was addressed to me by my college professor while I was bunking the class.

Question is taken from Closure Properties under Boolean Operations in chapter Properties of Regular Languages of Automata Theory

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The correct option is (d) Al of the mentioned

For explanation I would say: At first stage 1/2 L will be regular and subsequently, all the options will be regular.

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