# pumping_lemma_notes - The Pumping Lemma for Regular...

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The Pumping Lemma forRegular LanguagesThe Pumping Lemma forRegular Languages– p.1/39
Nonregular languagesConsider the language.The Pumping Lemma forRegular Languages– p.2/39
Nonregular languagesConsider the language.If we attempt to find a DFA that recognizeswe discover thatsuch a machineneeds to remember how manys have beenseen so faras it reads the inputThe Pumping Lemma forRegular Languages– p.2/39
Nonregular languagesConsider the language.If we attempt to find a DFA that recognizeswe discover thatsuch a machineneeds to remember how manys have beenseen so faras it reads the inputBecause the number ofs isn’t limited,the machine needs tokeep track of an unlimited numberof possibilitiesThe Pumping Lemma forRegular Languages– p.2/39
Nonregular languagesConsider the language.If we attempt to find a DFA that recognizeswe discover thatsuch a machineneeds to remember how manys have beenseen so faras it reads the inputBecause the number ofs isn’t limited,the machine needs tokeep track of an unlimited numberof possibilitiesThis cannot be donewith anyfinite number of statesThe Pumping Lemma forRegular Languages– p.2/39
Intuition may fail usJust because a language appears to requireunbounded memory to be recognized,it doesn’t meanthat it is necessarily soThe Pumping Lemma forRegular Languages– p.3/39
Intuition may fail usJust because a language appears to requireunbounded memory to be recognized,it doesn’t meanthat it is necessarily soExample:The Pumping Lemma forRegular Languages– p.3/39
Intuition may fail usJust because a language appears to requireunbounded memory to be recognized,it doesn’t meanthat it is necessarily soExample:has an equal number of 0s and 1sThe Pumping Lemma forRegular Languages– p.3/39
Intuition may fail usJust because a language appears to requireunbounded memory to be recognized,it doesn’t meanthat it is necessarily soExample:has an equal number of 0s and 1snot regularThe Pumping Lemma forRegular Languages– p.3/39
Intuition may fail usJust because a language appears to requireunbounded memory to be recognized,it doesn’t meanthat it is necessarily soExample:has an equal number of 0s and 1snot regularhas equal no of 01 and 10 substringsThe Pumping Lemma forRegular Languages– p.3/39
Intuition may fail usJust because a language appears to requireunbounded memory to be recognized,it doesn’t meanthat it is necessarily soExample:has an equal number of 0s and 1snot regularhas equal no of 01 and 10 substringsregularThe Pumping Lemma forRegular Languages– p.3/39
Language nonregularityThe technique for proving nonregularity of somelanguageis provided by atheorem about regularlanguagescalledpumping lemmaThe Pumping Lemma forRegular Languages– p.4/39
Language nonregularityThe technique for proving nonregularity of somelanguageis provided by atheorem about regularlanguagescalledpumping lemmaPumping lemma states thatall regular languageshavea special propertyThe Pumping Lemma forRegular Languages– p.4/39

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