Unlike the Pumping Lemma, the Myhill-Nerode theorem exactly characterises the regular languages. As an illustration, consider...

  

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Unlike the Pumping Lemma, the Myhill-Nerode theorem exactly characterises the regular languages. As an illustration, consider the following language: L = {ackabm|0 j 5 and k, l, m N and (k 2 lm)}. (a) Prove that the Pumping Lemma fails to demonstrate that L is not regular. In detail, demonstrate that there exists n N such that any string w EL with |w| n can be written as w = xyz with |xy| n, y 0 and xyiz EL for all i 0. (b) Use the Myhill-Nerode theorem to prove that L is not regular. Unlike the Pumping Lemma, the Myhill-Nerode theorem exactly characterises the regular languages. As an illustration, consider the following language: L = {ackabm|0 j 5 and k, l, m N and (k 2 lm)}. (a) Prove that the Pumping Lemma fails to demonstrate that L is not regular. In detail, demonstrate that there exists n N such that any string w EL with |w| n can be written as w = xyz with |xy| n, y 0 and xyiz EL for all i 0. (b) Use the Myhill-Nerode theorem to prove that L is not regular.