# Module26 - Module 26 Pumping Lemma A technique for proving...

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1 Module 26 Pumping Lemma A technique for proving a language L is NOT regular What does the Pumping Lemma mean? Proof of Pumping Lemma

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2 Pumping Lemma How do we use it?
3 Pumping Condition 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

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4 Pumping Lemma All regular languages satisfy the pumping condition All languages over {a,b} Regular languages “Pumping Languages”
5 Implications We can use the pumping lemma to prove a language L is not regular How? We cannot use the pumping lemma to prove a language is regular How might we try to use the pumping lemma to prove that a language L is regular and why does it fail? Regular Pumping

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6 Pumping Lemma What does it mean?
7 Pumping Condition 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

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8 v can be pumped Let x = abcdefg be in L Then there exists a substring v in x such that v can be repeated (pumped) in place any number of times and the resulting string is still in L u v k w is in L for all k ≥ 0 For example v = cde
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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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Module26 - Module 26 Pumping Lemma A technique for proving...

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