# 09.pumpinglemma.ink.pdf - CS 301 SEPTEMBER 21 ST – PUMPING...

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CS 301SEPTEMBER 21STPUMPING LEMMA
Regular LanguagesDFA = NFA = RegexRegular languages are good, simple languages to build fromVery common in string search and data miningWhat is next?
Regular LanguagesDFA = NFA = RegexRegular languages are good, simple languages to build fromVery common in string search and data miningWhat is next?We need a good understanding ofnon-regular languages
Regular LanguagesHow do we know if a language isirregular?
Regular LanguagesHow do we know if a language isirregular?Much more difficult to prove than showing it is regularRegular(x) =M(Decides(M,x)
Regular LanguagesHow do we know if a language isirregular?Much more difficult to prove than showing it is regularRegular(x) =M(Decides(M,x)!Regular(x) =M(!Decides(M,x)
Regular LanguagesHow do we know if a language isirregular?
What is the biggest constraint of the DFA?
Regular LanguagesHow do we know if a language isirregular?
What is the biggest constraint of the DFA?
Non-regular languagesA language is non-regular if there cannot exist a DFA which decides it
Non-regular languagesA language is non-regular if there cannot exist a DFA which decides itToprovethis, we utilize the pumping lemmaThe DFA can only have finite states, and this is the primary constraint on thelanguage
Pumping LemmaFor any DFA, there exists a numberp,called thepumping length, for whichany string with length > p, the string must pass through the same statetwice.
Pumping LemmaFor any DFA, there exists a numberp,called thepumping length, for whichany string with length > p, the string must pass through the same statetwice.What is p?
Pumping LemmaFor any DFA, there exists a numberp,called thepumping length, for whichany string with length > p, the string must pass through the same statetwice.

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