Given the language L={w| the number of a’s is greater than or equal to the number...

Given the language L={w| the number of a’s is greater than or equal to the number of b’s in w}

a) Using the Pumping Lemma to prove L is not a regular language.

b) Using closure property to prove L is not a regular language.

Expert Solution

Claim 1. L1 = {w ∈ {a,b}∗ : w has the same number of as and bs} is not regular.
Proof. Note that L1 ∩ a∗b∗ = {aibi : i ≥ 0}. Now assume towards contradiction that L1 is regular. Since a∗b∗ is regular, and regular languages are closed under intersection, then the intersection is also regular. But we know that {aibi : i ≥ 0} is not regular – contradiction.

venereology answered 3 weeks ago

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