Question

10 punts Use the Pumping Lemma to show that the the following language is not CF { xxn20AXE (a.b)* } Notice that this language is not the language of all strings with n characters from (a,b) on the left of the cand another n characters to the right of it. This language requires the same string to be repeated on both sides of the 'c. For example, if abbacabba and abbaabbacabbabba are both in the language using x = abbay, but abbacbaab is not in this language. For the toolbar, press ALT F10 (PC) or ALT+FN+F10 (Mac). TT TT Paragraph Arial 3112pt) %DO QEZETT, Of Mashups - tum @

Answer 1

PumPing lemma cfox CFL) iS Used to Pove thot a Langage is NOT Context fee Tf A IS a context fsee Language, Then, A has a PumPing Leng p p Such that any storg 5 whexe 1I2P may te divided into 5 Pieces S=UVYZ Such that the following condibrons must te tove DUvixyZ is in A feo every izo 2) IVY >O 3) IVX41<P *)TO Paove That a Lang. is wot context faee using Pumping lemma Cfers CFL) Ene Pove Usang contsadicton} D ASSume that A is context fjee i) E has to have a Peming lergron (sey D Ti)Ail Stangs Langer than P con be Dumped S12P ID NOW find a Storng §' in A Such that IS/2P V) DVsde s inbo Uv xyZ VI) Show that Uvixyiz&A fex seme ì Vi) Then cansdes the nays trat s can de divided into UVXYZ Viii) Show that none of these con satisty all the 3 PUMPing Conditfns at he Seme time ix) S con't te Pumpa contoadicthion

1. - ASkeme that Lis cantext fsee 2. PumPmg lengta ACCOncting to conditicn then L= fabtacatta3 abta 3 Dnde Langage inbo 5 rests UVxyZ U=a6 luR L={attacatba? Stang langtacn)-a y-ab 14 72 2-6a 1212 case I:- Ivxy1<m 5E9ur Casc2: Ivy) >O Case 3:- L=UvixyZ i20 i will take 1-2 L-abbabaç ababba *OUS ASSumPtzn is useng Becorse c' s conbe of Lohale lett hand Side and Riat bend Side Same Stonfes ovilable tt nt naw ne hove L'tHs=abBaba R-ES=ababba he will toyce v8y lales Anng like va y6 ete uvxyiz EL fog Seme i L-cxMzo8XESaVB3^} is not conbect bee
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