Question

Consider the application of the Pumping Lemma to prove that the language over Σ = {a,b,c} shown below is not regular: L = {aibjck: i ≥ j ≥ k ≥ 0}

First, we choose an input string w = apbpcp=xyz, 1|xy| p, |y|=k≥1, where p is the critical length. Next, create another string w´ L  to produce a contradiction. Which of the following string will produce a contradiction?

e) w´ = xz

f) w´ = xyz

g) w´ = xy2z

h) None is a correct choice.

Answer 1

In the given question option e is not satisfied because it is not in language since j=0 < k=1

Coming to option f it is wrong because it doesn't produce a contraction that it is not in language since xyz is in language.

So Option G is correct by Proof of pumping lemma.

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