# Module27 - Module 27 Applications of Pumping Lemma General...

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1 Module 27 Applications of Pumping Lemma General proof template What is the same in every proof What changes in every proof Incorrect pumping lemma proofs Some rules of thumb

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2 Pumping Lemma Applying it to prove a specific language L is not regular
3 How we use the Pumping Lemma We choose a specific language L For example, {a j b j | j > 0} We show that L does not satisfy the pumping condition We conclude that L is not regular

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4 Showing L “does not pump” A language L satisfies the pumping condition if: there exists an integer n > 0 such that for all strings x in L of length at least n there exist strings u, v, w such that x = uvw and |uv| ≤ n and |v| ≥ 1 and For all k ≥ 0, uv k w is in L A language L does not satisfy the pumping condition if: for all integers n of sufficient size there exists a string x in L of length at least n such that for all strings u, v, w such that x = uvw and |uv| ≤ n and |v| ≥ 1 There exists a k ≥ 0 such that uv k w is not in L
5 Example Proof A language L does not satisfy the pumping condition if: for all integers n of sufficient size there exists a string x in L of length at least n such that for all strings u, v, w such that x = uvw and |uv| ≤ n and |v| ≥ 1 There exists a k ≥ 0 such that uv k w is not in L Proof that L = {a i b i | i>0} does not satisfy the pumping condition Let n be the integer from the

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## This note was uploaded on 07/25/2008 for the course CSE 460 taught by Professor Torng during the Fall '07 term at Michigan State University.

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Module27 - Module 27 Applications of Pumping Lemma General...

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