Automata Prove that regular languages are closed under difference, using an indirect proof (leveraging the closure...

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Question

Automata

Prove that regular languages are closed under difference, using an indirect proof (leveraging the closure of other set operators).

Answer 1

Answer #1

Let Σ be an alphabet and $\bar{L_{1}}, \bar{L_{2}} \subseteq \sum ^{*}$ two regular languages.

We know that regular languages are closed under intersection and under complementation.

We can write Difference as follows:

$L_{1}\setminus L_{2} = L_{1} \cap \bar{L_{2}}$

--> Hence Regular languages are closed under set differentiation.

Answer 2

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