pumpredeng - The Pumping Lemma Lemma(Pumping Lemma If L is...

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The Pumping Lemma Lemma: (Pumping Lemma) If L is a regular language, then there exists a positive integer p (the pumping length) such that every string s L , | s | ≥ p , can be partitioned into three pieces, s = xyz , such that the following conditions hold: | y | > 0 , | xy | ≤ p , and for each i 0 , xy i z L , The Pumping Lemma for Regular Languages – p. 1/5
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Strategy for showing that a language L is not regular 1. Assume that L is regular (with the aim of reaching a contradiction). 2. Choose a string s L , such that | s | ≥ p where p is the pumping length given by the pumping lemma. The pumping lemma then says that s can be partitioned into three pieces s = xyz where | y | > 0 and | xy | ≤ p , such that xy i z L for all i 0 . 3. Show that for ALL POSSIBLE partitions of s = xyz satisfying | y | > 0 and | xy | ≤ p there exists an i such that xy i z / L . If we succeed to show this, then we have a contradiction with the pumping lemma and our assumption that L is regular is wrong.
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