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TOC CNF GNF Pumping lemma

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In pumping lemma it says if there is a string whose length is >=N,where N is number of states in dfa,then language of machine is infinite,but there is one upper constraing also. 2N-1>=|W|>=N Can anyone tell me about the use of 2N-1 here ?
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learner_geek asked Aug 5, 2017
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Given answer is (a) but L->AB i think it is wrong because A and B produce something else Previously, so instead of L->AB there would have given like L->MN M->c1 and N->S then it was correct . if I am wrong please correct me.
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