Question

1. a) Design an automata to accept {(10%)'li 0}. b) Prove that the language {o'12 i 2 0}is not regular.

answer B

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

LiS ReGlar7 l. ASSeme that 2 PumAing length ACCesding bo condition Let ì=2 then L={Q?,?c2)g= {01113 S DIVide LongJage into 3 PasS XYZ ० X200 IX=2 అంL 121=2 Stang lengo, h)26 case i:- 1X y) Sn case3--L=X y! zizo i will Gekei-2 001002=001C1)?11 case2- 1y/2| L=001 1111 case3: I will beye i=2 L= 00 CIURII L= 001111 11 Y Cfayled *) aus Assum Doren is uyeng re cause mo- of 's most be odd no-f is nat Aceend by Langage, so forked *) Becase 5 s hat muitiRcy of 2 double of o's tut at now TOIple. This TYRe nat ACONA by ou8 AUtomcta so It is nat delas xyizEL L={01/ 1203 1is not seiey
i am done perfectly by using pumpping lemma

Anything doubtful or not understand just comment I will touch with you

Please thumbs-up for my effort

Thank you and all the best