lo Sy ABla A> aab BAC Souk-y: Chomsky Nowmed fourm Conf): A Context free Frammoc is Sais Phe prvclucHens ane of phe Form APACE mae When A,B,C ane inv Ow In TT Conversion of given CES fo cNF! oer poieeny ae ae SABA A> aab | BAC | ah Ha above grammes, 52 Coed b> AB INCNE Bor Ac wm WF Let AIPA yen SABA Suan V | Q..DeFfine Chomsky {s322¢8154 Normal foomCc nF): Atse conver} The Fonawing cpa te CNFP 4o be in CNE TF oy Bie A> MA, BAC lor Ar AA Shen $s AB]a A> ALBEC th CNF R>AC CAL He prroctuetios 0 F CNF OOS S—> ABO A> Ar’) Qg>AC Ao by b Ba AA BLM: PS) V=dS,A, &, Av, Bi, Ar§ Tela bs © scanned with OKEN Scanner \ | | |» Begin INith the qoamm s-safa] babJé A->clo p> clb C-cpeE lt D—->aA]Blob WS Eliminafe & - forthe os . fe ohewete any] Umit poovcL iain 5s jy Hae veothing secre P ; ; iS Eliminate ony Useless Symbols in the wefutting frammevs ’ Seiution:- » Eliminaten of €- pooauietions : ae Im the given grammar coe ond Boe cs ond $5 hort BCS Nutable \enewles Ss anal bhb| b> —>p° . ae | DE D— Alab . ee ii Efiminatin of Coat ee me an possi Tn He coo 4A production ote cy aha|bBb|bb Aa B—)b C9 che | DE pm aAlab © scanned with OKEN ScannerSE Nani neuen of Lbetess gyn bels Dh Ha cibare Grammer ~C eloernof frroturec deremy nets 2. C 1S Wtettas JHerer frroolueHn are S-panal sab [bb Ama Rob Cee poe b> a|abo Th fyis proctuutin 1s Not reached aso) Sfowt Stake Haren paleo Ubcrd) poroctuLotien ane S— aha | bob] bb Ka R—b » © scanned with OKEN Scanner: a. Design a PDA tr the Tollowing language : Le iw) WEL a b3T3, Also domw the chemo cletq rem to + CHshve'led PDA. Worile the meterlaneous CLD) desea plion -for he shing 'abbbba: Sols L= Laba aabbpa, bb, abba, bab... F | 8: & Cqs,,2) = Cqo, az) & (4s, b 2) = (qo, bz) § (46,0,4),= 40-44) § (40, bay = (40, bb) | & (qa'ba) = Cqaba) | §Cqe, ab) = (Go, ab) | § Coy aa) = Gy, €) SCav bb) = qr, 8) & C462 > 2,2) 2) 42 Jaz bole o bz] bz @& aale aa eé €,z)z bb) € Balaa bby bb Ablab bal br Instertaneous Desexiplian (ID) for Sting mabbbba!: C Fo, abbbba, 2) |-C %o,tbbba, az) KC C4, bbba, ba 2) | | KK Cqo, bba, bbaz) K Cq) ,a, bbaz) 1c Cq €, baz) KC C qa, €& az) © scanned with OKEN ScannerConvert the following 9 CFG to PDA that accepls the same language by empty 6 ack. Es E+E /EXxE/€)/T —> Tal] Tb} 10 /n falb Given, Fo EE/ExE/©)/ + I> Ta/16/ 40 /1t}alb S: $a €,9 = Che EFF) ie a) (qe Ek €) § (Jo, & © = Gs ©) sq § & = Cyn D o~ D oO 2 | 5C4s, €,T) = Ce Ia §C4o €& I) = Ch, TD) & C4. € DT) = (qo 1d $C we TD = ads) & Gs €, LT) = Gs, 4) & (qo, & TD) = Ga b) & C4, 4, 9) C4e, &) | S C4ob8) = Cqa &) | § GaGcod = Go €) § Cw IY = Ga €) § (qn 1H = Ga § C46, 7k) = Go-wye) € (qn 0) = Cqa $ C4 Vb) = Cqo For non - terminal, Foe Tormmead An & § Ch, 6A) = CG) S@,T ,t) =e) © scanned with OKEN Scanneriva Shawkans Vor peeve b Shivas 7c SIERO @ Show that the language L={xEfay*l la [Oo isa perfect square} 1S not context- free. Statement: Let 'L’ be a context fe languagy, | then there exists @ constant n C pam ing lemma, | Length), ach that for sbing ‘W' “m L Wh bk \Wl >n, we am watln a6 | We uvxye Such that | 1) lvay) sm | WY) tvy) 2p Certs vor y ‘a rean—erply) | (in) ¥ pi2e the Sng uviayiz wom L | Cc Shing WMA “IH 4 lemguage atti poping Y amd y). | Gw L= XE CaNF]p xl 4 perfect | en: Ls D¥ [Jacl va Agiion J | Le oon, 1616, NG, - } i Step: LeL'L’ 16 the context free | cepted ‘by the PDA contains the vr abe ° let sting = 000 }I)o0) EL Step2: Note that length of x, Ix] = IT 2n oe NEF and now we can split j such that ae : wt wg? 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