Regular_Pumping_Examples

Regular_Pumping_Examples - MoreApplications of...

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More Applications  of the Pumping Lemma
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The Pumping Lemma:  Given a infinite regular language  L  there exists an integer        (critical length) m  for any string              with length    L w m w | |  we can write z y x w =  with                        and m y x | | 1 | | y  such that: L z y x i ... , 2 , 1 , 0 = i
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Regular languages Non-regular languages *} : { Σ = v vv L R
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Theorem: The language is not regular Proof: Use the Pumping Lemma *} : { Σ = v vv L R } , { b a = Σ
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Assume for  contradiction that       is a regular language L Since        is  infinite we can apply the  Pumping Lemma   L *} : { Σ = v vv L R
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m m m m a b b a w =  We pick Let        be the critical length for Pick  a string       such that:   w L w m w | | length m and *} : { Σ = v vv L R L
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we can write: z y x a b b a w m m m m = = with lengths:
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Regular_Pumping_Examples - MoreApplications of...

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