CSC433_Lecture 3_07.04.21.pdf - Theory Of Computation CSC...

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Theory OfComputationCSC 433SPRING 2021LECTURE 3 : PUMPING LEMMADr. Basma Hassanbhassan[email protected]
Non-Regular Languages4/6/2021CSC 433Spring 2021Finite Automata have limitations, they have limitednumber of states.Certain languages cannot be recognized by FA.Example, languages over the= {0, 1}:A = { 0n1n| n0 }B = {w|whas an equal number of 0s and 1s}How to prove that certain languages are not regular,i.e. cannot be recognized by FA?
Pumping Lemma for RegularLanguages4/6/2021CSC 433Spring 2021Pumping Lemma is a theorem states that all regularlanguages have a special property.The property states that:All strings in the language that are at least as long as apumpinglength, contains a section that can be repeated any number of timeswith the resulting string remaining in the language.Any language does not have this property isguaranteed to be not regular.
Pumping Lemma Theorem4/6/2021CSC 433Spring 2021IfAis a regular language, then there is a numberp(the pumping length) where, ifsis any string inAoflength at leastp, thensmay be divided into threepieces,s=xyz, satisfying the following conditions:1.for each i0, xyizA,( xz, xyz, xyyz, xyyyz, …..A)2.|y| > 0, and3.|xy|p.
Pumping Lemma Theorem4/6/2021CSC 433Spring 2021Example, string s with length n ≥ p
Prove Non-regularity of a Language4/6/2021CSC 433Spring 2021Pumping Lemma is used to prove non-regularity of alanguage B (Proof by contradiction).

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Term
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Tags
Formal language, Formal languages, Regular expression, Regular language, context free language

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