Question: Prove that language = {# | {a, b} } over the alphabet = {a, b, #} is not regular using the pumping lemma. Proof. Assume

Prove that language = {# | {a, b} } over the alphabet = {a, b, #} is not regular using the pumping lemma.

Proof.

Assume that ___________________________________________________________________

Let be _______________________________________________________________________

Let be the string _______________________________________________________________ is a valid string because _________________________________________________________

Consider all ways of dividing into , , and .

Case 1: _______________________________________________________________________ _____________________________________________________________________________

The pumping lemma does not hold for Case 1 because __________________________________ _____________________________________________________________________________ _____________________________________________________________________________

Case 2: _______________________________________________________________________ _____________________________________________________________________________

The pumping lemma does not hold for Case 2 because __________________________________ _____________________________________________________________________________ _____________________________________________________________________________

Case 3: _______________________________________________________________________

_____________________________________________________________________________

The pumping lemma does not hold for Case 3 because __________________________________ _____________________________________________________________________________ _____________________________________________________________________________

Thus, the pumping lemma does not hold. Therefore, ____________________________________

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