Question

3. Decide whether the following language is a CFL. If your answer is “yes”, construct a CFG; if your answer is “no”, prove it using the pumping lemma. L = {xayb | X, Y E {a,b}* and x, y has the same number of a’s}.

Answer 1

Pumping Lemmacfor CFL) is used to prove that a Language is not context face * If A is a context free Language, then, A has a Pumping Length's such that any string & Whose ISIP may be divided into 5 Pieces 9=UNXYZ Such that the following conditions must te tove Duvixyiz is in a for every izo 2) Ivylo 3) IVXYLP * To prove that a Lango is not context free using Pumping Lemma (foro CFL) {we Prole using contradictions 1) Assume that A is context free ii) It has to have a puning Lengon (Say D 717) All strings Longer than p can be pumped 1512P PV Now find a string & in A such that 15127 V Divide s into UV X Y Z VI) Show that uvixyiz & A for some i vii) Then consider the ways that I can be divided into Uvxyz the Vill show that some of these can satisfy all 3 Pumping conditions at the same time it I can't te Pumped Contadichon

-- {xayb/Xyc {16} * * 317 has some nook as Ashume that I'is context free "Pumping length Accending to condition let x=aab yzaba L- & aaba atat 3. Divide connage into 5 Pasos UV XYZ L=şaaba abab uraa lul-B1 U V X Y Z vota IVI-3 X ab 1+1=2 String Lengthch)=8 y-a 14F case 1:- luxyl en Z=6 1217 558V се - Ivy > 0 BO cose 3.- Lauvixyiz izo i will care il L-alastajabart Laataba ataaf x fouled =aabaaba ab aah x heyled *) OS ASSEmption is ugeny Becase right now we did not have equal no. of a's in x 87 x-aabaab: y = afaa 3 feyled 4 a's 3 als uvixqizal far gone i =sxay6lx, 4E2046 * 8 xyhes Sane noof as is hot Contettre
i am done perfectly anything doubtful or not understand just comment I will touch with you

Please thumsup for my effort

Thank you and all the best