Unit-ol ® sonatas Computotion $-Computoton 1% Quy type of Calewlahens that includes both Avithmehical and non arithmetical Steps crs fellows a1 Well cletined Models - pres aMoshefficleot 2 Moet PoisevelMealet pide: , . Digital Gmpuler 1 Bosed on “Tier Machine Fede tte) aoe DOE PUFA) PCPPAYE PLLOAD=PCTM) where P 1s PowerFiarpose of TOC CTAPL3- This Course aster the fllocreg quesort — What ave the mathematical Properhes ob Gmauber Hy) and Sra — what 0 Grn Oud what 1 an Ago ? Can be give rigorous Mathemabial clefinihen et hese nojehon ? . ~ Whatane the Limtahen of Gmputers ? Can ** Everg thing” bo. @mputed CAs we WillBee, the Answer tothia queshur 1 No» Be Of the theory of Gmputaten: Develo Mathemahiaa! Madlels of Gnputation that retest wea world Gmputers Basic’ Ie. A Sygertol vba mark, Sign on Any Pictorial vepresentahen Tew bate bluldeng block 16 Coy be « ne Oy jenny tae y Vy Mog Orbe 2-2 C2, 22616998) ete: Alphabet C$)‘: Finite 2ef of Symmbole a Bx. = SA, O--Zajb--- Ye ie ° a } ¢— Grammar Zbme Boa} sg Selec = $0/1,2,---9, 03 . Siig? £51 90 8 Bod m Stalig s Fintle Sequence of: alphotete By +f Le 49/53, ae £2.06, 20 ab ba aa, beb---f Sz 3912, Stongs= Ef, 0, 1,00,01,10,11,000,001--- 2 “4 ZF EAB -Pah Ft Sho = § Automate, Theerg ---- Lengine} Stn = # alphabets th te stnng éxl--. Shnky = Ababa Ther Vaebe] = 5 ek Orn sinng 2 Length = O Gscses Jele [Ale al e0 olePS = $a,b2 ® «Hoe M. Stas a} Length 2. Passible over i > SZ = $a,b3$ab b= $Q0, ah, ba, be} =4-stigs Reseible ~ Hod Mow Stags of Lengthy 3 Poastle ore 5 = 2. re = Fias chtetihesieaantpaaatsiat beb,bba, bbst = & Strrgs Possible . “VG Se $4,663, How mauy stn 4 se 2 feyble overs. ZL = RF, b, C$. 4a, b, C2 = Fag, abac jbg, bbbe,ca,Cbce 3 Fino May Stomgt Pestle of Lusty 10 on = 1=]" 3 Le or empty So Pudered 2 it = 30,03 ee. 39> Seofallsinpat Lots0 ones = 34) Sahoo 1 ce) af al) shius one lel= [A= JAJ=O 2 5 sani - nn of Lego 20206=0 Soe Set of Hl striud of Lenth 2 ov 5 Stang Con 222 TSH FG, bab} « $ag,ahba, Lb} Tie Setofallctmys af lnth 5 ever5. : 1 F235. Fs $4, bh3qb bas, Sb: Saco, aeb, aba abb bay, bab, bby, bbb} =" Setef a) stone of Length W = EZ ZFS 7 1D times Contatenations Substring’. Consecutive ol taker trem a worl or Shy; EX. Stnng = abcd AZ akc t Erabcol. = Abcol J 0. w 7 Abed = @ stat nyse? Nowe: d Shing Lengtn hn Then No - oP Suabstnigé= nent)Note: et cotter Oud 0 hn ef Sabine shee @ Of Length K = N-Ktd ex Wz Q000, No-a 4 Toled= Ex. AXIOMATIZABLE , 2 Total Siabshrgs = 2 Sol”: J- Length = 13-2-l=1o0 TB ohaa’ = acne = BO Aw — Refes n \B the front Poh Suttize TE Wt kao Paste ane od Of Stange, tf = Ob e abe! tr bed abyd abe abe Prefe. = §2,0,0b, abc abed Jw]en Thes Noved Prefixes M+! Suffice 3 E,0l, col, beol, abel f + Docker 44 |wIs hy Ther No-efdutlin= n+] Prefer Prefer Ze Mab AReS poo, tutte SerdrA, sab toe = $8 jd,cal beat Reverse’ .f CO= akeol . LoseoR- oT dcba, ag Le 29" 70, Leet. gba nzotfalindvom 2. R : ventana 4f O20o"2 0), Then wr Palinohom aie . , Bx. nitin, abba, aa, 042,0,b, bab, bb, bbbb, etc- If |W] = Even, Then Even Length falinchon Str d |W] =0olel_, Then Ode! Lert, Palindrem Shy Concatenahion- “f WE AbG, Wo = 2tyz Then Wy Wo = aber, Wo:Wy= WY 2-Abe , COSTES ner Commutahive- Ex! 2} Wea we Ww nab.ab # aabb (2b) W3eW-WW = @b-ab-ab tana bbb (9343) Ex! Liz 3a" nyo, p= $4" nx0 Ly-ly= ZA [mmzol t Zab”, nz0} BI" Lyz Ze Gaa--% ly= LE,b,bb,--- 2 Lb 3.€,9,09,b, bb, ab, ab4a2b 26>... $ Lyle Baran) nob Simi 4 Le 29%b), nx0} pan amet # yanun.an” |nz0} Bebbl = gomumare. bE ]mn 70 f Mclean shes cloth ip 5 = Sa,b3 x. Suz! v xy s8U Ft ee — YF y ee FY e.o,b naa, ba bb, Aoa,aab, abo ab ba, ba, boa b= stata posible sin ofall lngthowe 5 de Ewayehinge a 4b Dnivecda) Lowry Grnplete fet of akbKleen Positive clammy 5 = $q,b2 @ 3 = 38,5, do ab, ba,0b, aa, aab, aba, Lb, bar, bab, bba, bhb-- =~" ¥ ste $a,b,09,0b,ba,bb aa, anb, aba ,atb, baa, bab, ba, bbb -—--- wen Grrasmmay Set of rules te Provile vail stings 9, Rema larguage Tk 5 vey Wnportant we wil) See 1h ctelail tm the Te agaist Colleckon of Strings oO Feo) ease 3 Ex’ 4 S= $4)4 Finjte Fe § £,0,b,09,2b)04, bb, 00, aab,asa, ebb, bae, bab, bba, bbb" t L, = Setof all chong’ of Legth2 or, = $.Q4,ab,ba,bb} = Sebofall sh = $.at0,a0b,ana,abb, baa, bab, bba, bbb} Erfitbelongee sy a1 shane Stott wild Gomme C E § t,09j Ab aba 208, aby Abb of Lg = Psetafalishn eal weil 0,000 5 bac, ob8, bas, aas, bba,--- of Longty 5 oveh = NOTED /$ [eo = Complement * ob. Le VeePbt= othe STH DEOnE, oie stetees Of ee be mene’, Glee S ee ae le Goyaman, aad abe,n~ kesebap an eri Sed IS OO find T=? Le S*L = $E,b,ba, bb, bab, bba a 5 4 : : Language vwathiel 24 nok Sart With &B= Brey eae EE Enphy Shing or Zerp Lengts Shing. ie po VIZ VIB eee 0 Ca dhe gudtud See =4£,¢, 64,96 =$é, , e) fee ay * =fevg} ete eovelve ve----@ ete Evevee VECE “DO ete EVEVEVE- = perre Stole Ary Znleorad Gortguiaon afte Sopher ab parkudet hime ce A Stabs defined & et op toe Spee oF 4 Paw of-heme” a ~Inikal state C>7) Ba Umperate ene ela a (46) = ONee 4 “ Fina! Sted NENG oO} - Trap Cpead) stetr naa nel stake - Unveachable stale” al 5 0 b - “Trop of° ey 3 Finite Automals < Finthe Autorrole CFA) 1s the Simplest Machine * repie Patios. The fine Aubrnale or finite stah machine 13 an abstract machine Which have five clemebis or tuple Tk has a Sek af stata anal oils for Moving from one Skah ts anuthet but ct cleperde upon the Applica! mmput Gye! Basically it 8 an abstad mode) of digital Gmputer - Formal Dehnilion of FAS A hnile Audgmata gael hem ‘eaiphaber a Initio he 6. Fa= €Q,5, 8,%, FD T— setat final Staliz Finteset Trastharfmchy FEO wh gh of stale 8: X59. enw Block cliagrom of FA ngiat a jock ciagyam FA= oe Seo > where Q: LAB, i Finite Merny TE Zqybs ; | forfiniks I= FAL | 1 Grol, | thats | reall i Firite : - Finite stat. Core! Application of FAS 4- As @ vecegnizer— 2- Lemical Analyzer Implemectahor Limitahen © FAs 1 Memeny of FA ve vey Limited 2. Tk Cannot store or unt sting“Types of Finite Autemots : @ ore A anna sine Finthe Automate Fine A Finke Automate Without oubpat veirth oukpad Desir NN CaDpAe NFACENFA mg ape y, Acceptor oR nizer eel. ica!) Tnpleme statienr Simple Design Tite for Digiled Coch Dec yy Deterministic Finite Automate CDA): paige snikelstot te A DFA oe bervepretented by a S-Huple CQ, =, 3, "iE atten Remares:. Wh Finttesel Pepweghentunchion FE oy Leek onh ove Onis next Sale es b} Stakes 5.042 78 Lt has no choice os vorcemness ' : > Giver tre (wer) stati we. Kom NOTES Why Ded Configuiahan nok \whot the next Stab ull be Allowed tk DFA ! L > Dead Contiguiahen net allowed pyr AA S* become DEA 1 Gnpleb Syston ian Payee rrahal stabs Configuurehar F Ex: DEA = o. a,b Defined mA Stated tt us no 7. Finedstals *6 e DFA wy hie . DFA= (8,2, Site Dn" Whew A = 3A 1,05 Gs Yo ne Da ee elle : Dead Confauistt jon OTE: Hota te Remove Deod Ganfguiahen{ i “Snes Addl dnp or Dead state euyerre “y es Valiel DPA gvalid trite funthonNon i Detferminishe Finte Automate CNFA)$- NFA bs yee i Cas ‘yeprerer| a DypAlphovel By Selipe = (Se Ste Sebey inal States Fink Tnthatsiete =P" pawwaset Trorsthew mee a function 8:8x 52% on MA anal) > In NFA, Giventte Comentstat there couse ee next stabi as Lo 62 b ‘0 # multiple By (a os Stobes bos Me > The next Stat ™) be chouepabreninn > Al) The next State fat) may be Chooser 1m faralle! > Deael Gonfigutahon “aiteeed 1 NFA, Ex! US) fro > E- tonhn co eee Qc ee eae Re NTE! why Desa! Gon: Mireed a tunthor §:8.X23 2 va ta, Ze — seit NFA Be Men ont Sox 18 Co-dawrate Dera hana Im Pander theta Wity Dead Grfgussher Mlooed raiDifference My DFA & NFA‘ DFA d- No Choice 2- E-Move net al leroed 3- Dead Conrfiguahion 170 Ad jnoed 4- Desa) State mneyyba requlred 5- Number of nest Sent 18 one a ’ ‘ayo G-NFA 1b Easy 4 Grtrut 7 - Converdlon NFA ta DPA has atnnest 29. stay te 226 siete @- Lmplemectahen of DPA Tesuie m Ore Space 3- The total Hime vequived forrunn uy input String im DFA 18 Less ex. ee | o- [AKTv2018-13, saves] NFA L Choice atiwoed lo- & Moves alleden} 3- Deaol Corrhguiston ai}moed 4: Dead state 1 not requires, 5-Numbet of next stales Carr be Zex0 20ne., o- mores a OFF a BS IG- DRA 1 rretahvely hippie & Conroy y- 12 Q-steba ye NPA @-Tmplemectahen of NFA requires lese space then DEA The, tofad me vequt for weaning cay input Sinig yh NFA ia Lasger - i Si AXT PA td- Ad) DFA OM NFA NotEé:- rd L- NFA 8 2° Ev Pui DFA dor Fewer mame’ Ne, ot stabet in hoe S! OX Sd 2% ox PLO) Not ad! NFA at DFA ne why Become DFAIS: AXS—> E+ QE2P seat ora Mpa Ss AXZ225 9, NFA 2°E 6 Net all NFA ase DFA more general machine as Gmpared ts DFA DFA 18 0 NFA but mace. Every NFA not DPA, Bub There is a NFA, wan 3 LOWPA) = LEDFAD > PCNIPA) = POOR 3- EEE ONS yecaube There 1B an Equivalect Dra fr Eve NFA NOTE! No-ef states wo NFA =m, oe Winee 3 DaASN,Represeviakion of Finite Autawates- @ WAAAA AANA Trans hon Graph’. Fannthor Table b , DFA! 3®* * _s Dra Oo. b 8 FP eAIB SS Pa, b ¥g|8 ® oe a a,b NFA! Soe a Qe] & ped eAIA® — 2 Acceptance Finite Autemale:- Acceptance by DFA! DFA IM = CO, E,5,%FI5T” Lomas £3] O8( %,wergee o Stig 7 ts accepted by Qe DPA Mal 85, 5)40F- S# (40 2D =A WEF Example: DEA: M “oer a Lebstnig weabb o 1 IEdIB.b) = Ber, Accepted. ECA, ebb F S(B) bb) ” wah sopablere Biuce- Diagram of FAL Finitestat:Guhel [Accoplace hy NPAS NPA M=(6,510) nF he TORTS SH1 O80, ONE FO fete @ String ah aecophed by Q NEA T= (O)2,5)40 FE) ef Bran = atleast ane ine SS les o,! or@ myer E(w, 02002 5 (4s, L00d +5144 004) OUR) oL) (40,9044)—| 0/43/14 2) $450,444 3.04} = 14. FB, Mleaat, te le ArentDRA-Designing 3- “if S = $0,532 ® O-u. Design DFA for Empty Language , Le Le@es2 i Q-2:. Design DFA for Emply Shing » €-€ Le&=$e3 rae Se aa NOTE! Hf initia Slew alo Fred Sak > Twopsta Then E- input Acceph bak net write 1s DPA, OB: Set ofc! shri short etuth 0, evel S_, Design DFF L = $ 4,09,0b,0b0,094,abb,---- -~ 2 =acaryyt Totten Heer Infinite thes take Smallest str bul tf Lavage String for DFA Desgni Te sad coroe wrahon bg Dead Grnfigeushes not Alleded 1 DFA - ‘ap moves accorelins 1 ie strings dl wth 0, over. , Design DFA Q-4t Setefall lie 2 = Catusta Le=¢ Q, 08, ba, 269, baa, Sohrke ,O ot BS" Q-5: Sebep al Stony Corton a on Substring Over > Design DFA [ee $.0,00, ba, ab, aba, baa" z = Ca abota cates go ag te 88"OB: Sebep au! Stringé Shaub with Abb , over = Des igo OFA @ Sol") = Abb ext = Zabbh,abba,abbl, abbabh,---2-apoiasi nf belongesy® Smalleststring- Firat axe Smrajfest String, Atecthat olefined! Renounig In} Remove dead Grfi 42 , S NOTES Eveuy Shing pak wns = pat od \ “Then minimue Ne. =|WHd: ne BeF:-Set of at) Shnngs end) weds abb ove & Design DFA Sol" 7 XXX Qbb = Cassy anh = path, aah beth abbath---- ou" Sirallest \ ‘Stony Nore: Every Shang eral euath w) Ther mmm see DFA = Jwitt . QB! Sebapadl Shugs Gotan abbasa Substngt oS. Design DFA Got L Sone abbrxx e(onsSbub (ater $ anh rab, bath aatbe, abbabb-—-} Comphemect } =, PA. Se sa,bt Fairing Subehrig.abbQ-9: set ©} atl Shi Stok with 0 aud . eee He. Sol"2- Fret tind Lavguage Set L=$ 0,00, aba, abba, --- = 8 $2 Qb : we > Cs} a,b G10: Seb eta] shingh,Shavt with 0 axa} eral wth b,OveLS. Design DFA SoM La Sab, ab, abb, web ~~" 3 a a b b . a Oy > O-ils Setet.a} strings Stour one! ere) with Atfereot Symbel, overs. Design Dra Sol! Le Sab, ba, ack, bac abeb,- es : Q2 Obert MOSES = ei : Gl": Lig= Ly = $ €,0)b, aba, bab, aad, bbb, 2 new Dra ter Lio. Lanzuayt 8 Complement ot Ly DFA CM),.So Fee Opener ee a Noves-f Complement of DFA® (B/S, 5)2)F) 8 DFA = £8, ye ETE Means Change Final aede, Sales a4 norfinel Stakes and non Imp tinal ‘taba bs Final States, This Concept 1it apphcatle for DFA ply not far NFA, We Will see Latet, m detalls;OB: Design DFA ,ovet S for Gi) 1. Even Length sti @ Gi) 2. odd Longin Sti Sol”. Even lerain Shrine » L¥$£,00,ab,ba,bb,--- 3 Covra:. 6 fp ab Ce engin shins. Le $4, can,cab,abs, abb pa, bes, bbe hr . Ab DFA: 28 ab O-14t~ Every 0 follooe! by ableas! S/R 2b ae LS. Er brbbytbh--- > abb, abbb, abbapb,----- b 1 Qc15: Bvety O never-telleed by 26 sol? Lis #Lias Both are defferet Language,B0 n° need ts Grnplimest Lig = 21% ga ja, aba, by bh,ba,---" 3 DFA: Gb : a> 6)O7O 8 ~ Trap state G-lo:- Set oF all strings either storhr4 ith AQ OF bb, over 5 L= $00, bb,aanaat, bba, bbb, -- a3 DFA: @ CapO-#: Setof all Shige end . a i ; sign DFA y With either QQ oR bb, Over = @ Sol t+ Firat Fire! Longuoye Set L= ry L= $a, bb, baa aaa abb, bbb, 3 Q-182-Design DFA -br the Set of shins vera jb} Sucbtiat Length of the © wo eetaal tp Iwle 2 wilds DFA! ao DER! a 4 BEA g COE = oontt 3 lb if 24,6 Le $.a9,0b,ba, bo} LeSaaabpephar-—} Le 3€,0,b,a0ph Mat _ heats 24 =4 Necpriat 23 No-erd steates 24 NOTE? JoE> 4) Sta coud Lops Sloat DI iwien Lid win dd) wlan ntl ntZ Minimum tle stohaz N42 n+2 O-19:- Desig DFA Net te lott rope caielg eset aU sings rer $a,d} th Whieb 2” from BHS 4 0 Sel"! The shrigé im i 2 dl rom Lid * Le $.aa,ba, aabbab---° £ = (a+b a(a te) Dra: a Be4,b-20% Design DFA ob the Contayning the Set ef aU sti ) . OWA$.0,b} 1) Which 2” Nees tts “a a v ® Sol"$- The Strings 0» Which PF Lact cymnel Ub a! au rs L=$.0a,ab aah, aug, ania Bbaban--Z 2 Gia Cor ooo | from RHS NOTE 2} nth ee 24 nF rsymnte h ig O Then MivNo-e4 stakes = 2. By! lf Job Syerbel from RYS 4b O- “Min Ale-ofstahd = 2!7 = ]024- Ant Orn. $4, 63 Such that Length ehthe mod 3 =0 R_ mmistbes=S L%,% 42] a = nd L= Sw|twimeds=0, we (a,b) © Fe Bor eomindet Sol"! Find Stings =< £424, 09%) aba, Mini.staber = + Q-24:-Design DFA orth Set of sinig Siig Iw] & devise 3, xe, Iw] oR ab, bas, bab, bbe, Eb, c= fy —— : DEA: med mM, Then minimus No-e4 Sales zm cased} L= Sw |mlaned g 0 ECAD 2, Meon nofolivalle by Bo Ten Fra States = 3% % F 2 Swliwjmeds=L, Wega by}, mene Remain ghedd te LoTher final stabs = £4} Cate. Bt L-$w | med2> 2, 0 € (a5) } means yemuirde, ‘Ghat be 2.5 Therm frol Stoke: $n} cote 4-4 Lez w ]}»} mala> J, © (96) 2, Mean Kemal Shedd be gresta thon Lee yemunda 2, Ther Anal Skht = £%4(0-22: Design Dra for the 2L2 SW [nyo medo=0 n,c0) mala 20, & v0 €-(0, b>” 2, Means Na(@) clisrisscle by 2and Nycd)m 0 14 dive bys Anst- L=$w|Nnglormedz = 0 LEN, mals 20, WEO,bI?? DNL alte Caliah * $m = Remajndr-=$ oy!) 22 Hyper WA Wee. ndet=$0)1) a Mod m Led n., Ther Where: Nqteo) # Novas amw Mini.No- vf states =x": yw) Nevep br» | Meant Camestan Prolucl $02? x4o/l27 Total States = $0/12 %$0)1)23 = F 00, 01,02, Jo, 14, 123 07 On OF TT) ot Lb ae ooo Cosel iy Nala) mo is chivyeitle by 2 aval Nye 6 dayrcitle ys Then fina! Sal = Zook Cone tf Maglio) n © 14 divisble by 2 andl Jo 16 not Levsisle nse Pinal Stok = $ 01,023 (ase 2! naca)in 0 1s notdavisiife by 2. cul Tteay into “ Lb chiyssble by 3 Then finol Geka = $ 10} cases: ef Na t®) hed 18 hot Livisule 4 2 anol Ny (27m wD 13 algo not dyrsele 4.3 thee final steber= $11,122 Nqlodmed2 7 nyfwored 2 Then final Slates = 5 10k Carec: +t Nal) red 2 < M(eo) myed 2 Tren final les © $01,029) inal obs = § bold} Core 7, tf Nqlo)medy = TyLw)ned2, Ther ° Cate +4 Nal) mals F mytwymede, Then fre stata Eos eA A tO A A I I cae5:(0-932-DesigoDPA for L = $y] nqltODmeds = a wer et & Ans +- Minish required = 5x3 Tf number iw oliyisible by SsTher Fabris 2] mod 1 dood an n Remosnda = $y a Ten mini Er mint od Total states 1n Ls $d 22 KF Op 4/2 $= $0002 tmunizaneee 02, 10)1312,2921,22F aa 2 cates jest ek aero Q4*- Le Sw Ingcvor —nye2>| marie =O wetayd) 2 Design oe Meank Ng) aud nyge)m Goll t= Ng Cw 4 Mor ef QR nycer! renee bre DFA tor: mare SPOS be raubbiole of % ae Qo: for zero Remainder shate. Fe ee, Le $10] tnceay—neceomeds 70/0eje Z57her pal states = £%ad Carer’ of L= S72 ee Final chae = £94 F aie Le sy] a Hache’ =$% 4 See. aco lmala>sj0ecab) L Sod ‘sales $ 4p |medac 2, OR4bNZ, Then ol 3 Fd. ,2 €(9/8)" k Then0-25%- Desi " - Design ali fo no == Fol} that accept e Ly Even No-ef 05 aud Ever No.of d's 11,(i0) : No- ef Zero I,(40) : DFA: Ny (eo)! Ne-ef one. Ob if Batscondikers & 7 Ever ROE Boral oh $03 0 : Odd SS yep Ai) Even No-ot O's aud cdd Nove} I : States DFA: VE. Both Concha “= 9 J Tresane (0 2 Geog 00 L ay > GB) Ode No. 0's ond Ever Novell's a ) ats + “f (deen | aud EverNeef J's TRUE XO Aine Steals = £003 ee te” wee REA] bats Grdior CAA Neat Os” awd OAANe-of Je TROE Be tinal Sta = Z00$ — dl No of Ols OR Oven Me” US reget tne vy ou of t OE a] either BAA Noof Oc TROE DFA: OR Ever Noet J's TRE Bo tral Stal as = £ €€, 20,008 ie wee tat0-26 2+ Design @ DEA for accepting the e L$"? > Ans*- Far Creating Dra fer Laue ® merge Lie Pinan elementary mathemalics Which sone eventeven= ever old Fodd = eh Tere 18 2. Cases which wesulks 1m acceptance of String! Le If both in ond 1) are Ovth then ther gunn wulibs oven Ae Af both m and 1 aur odd then ther Suen Wil] ba ce” Aang, otter. Cmbjnahen results nthe sozechen of input sity: DPAE CB 5,5) FD whet = $.%248. 95,04, 8iteAet Fe 84b4d = B%E Fe £%,%s, 3 Si: tromathn funchor (27% Design DFA forthe Lovpusge ‘ Le Swi mitod=2) NDI 2, OEE e op GP DFAS (G2, S/%oiF ) vohen, : Oz$% M95 04 Aste Aa fe, tater, 224 bk We E%h Fr $%5} \ 6: tromtihar anchor0-284 Design DFA for modulo. j in bite Bee Bain fe Coos 3, ® ign L= $sldesymeds =o, where 3 of s, seco,t tt f ee fs Grantee: uta bin tbe ml es FB bahay untengion sf opeop: Decimal) Binary 1 4 Opt ise, Then nunter clmble of review 5 ; to gud YplatisB tren ¢ zs Ld ject, of Previans mame 2 4 100 no=2n 2 5 fol: na cont 5 6 110 oes - 4 til 8 1000 ommaindey COvk, 2) ryipieloedisinat bh ED —— Le} nunbet sin at % Stele ‘Babi noc ane 2ryag Ol aeada steele ne common rege [gota 2 stele, Ound noonumb.at 2 a2nel] ° SD ® Appl 3 oad 1 at 2, Sak 2 \%3=2 [gote Jabs ancl wea np-at 9, Seantans= > [eptelat a2 * -] C2ned or ent? Camel = 4k 3 D(4nt3)ng20 [goto qq ste] ° Loe L ‘Shorteub Fill in Cyst. / to andLata, stab” ore Siri lady SPR pet a a ci aor a 4 (ant2)0= on «Gnas (ante )7s=2 Tet) o Q4 Be aes A “Feonas han Tob Lage gs Gf Le ES|RS MEAT ter Gl lt 82, case! f Le # eendi2 tm Soadsiet ne z! =i 3s]d(s { 4 1405) melsSPL3 Then finel shalt $9559 a. een ht0-28:- Design DFA ter 1 23S] dicymeds=@, When dee) ut deeimal vlna 2 ts and Se(0,d HR [AKtv-2017-1g, Marks-0F] Mal States = = 3404 Coad 5)" Modules machine, Basp 1 bis ee Poet Quehn [use 8 posing hoon, nl=2"+i] £ abet ai > Bae rat $ 071121 34} Ase tis tn 0 Petals Use, Cyebic ovales pon ean Qo-> 929997 94 Rv Q-30:- Deeg OFA fr L= $Sldtg) mode = 4, uoheiz lis \ui decinnal Vidas of Sand SEConytOrsi Desgr DFA, Modulo-d: machine Pete Thay. 2-2. (Mod4) S Ans', (Mod.4 2 ° Trina Numbes input Syrel ESO N2 yee 22Fo) 123 andl: Mod-4, Machine 50, 4- States ireol $ % 9 90,934 Recimels- Tein Ne « Note In Trina nowpten wh 2 2 eda z art nie 3ntl 7s 10 n2= snt2. at Ls {, - are Jew Tanata Noa] apoly % Ot LS T76° ; os Nos Thrice Preset -+f' aad ei ob “then Na- Thrice +1,0F Peiviont hon 9 100 12 at LS@ Then Ko Trce-+2 Of Previn Letnoe 1 at % Stabe = "HOE BM jnged C0] : nls ante La] naz nt 2A 274] WNowoNe. antl ab set: : Serio = antara4 S gots da Sink aud Naha Her, Cans) = raha AO, goto fost C3nt)2= nth pd Al, gofdset Ache. gntzerysies Cantar gnt 670472 Canta) Le QnePr4= 3 antz)20 ant 3Y%.4-0 Ard Ho- ant abfpsiab: aon BEN col contajte 2Pntlo%a = 2 COnt 3)2 = 2INENL4 HBO-32%- Design OFA Pr Medulo-7 machine Oud Base ui Triraty? “e Desgn (Mod-4). res) Ans'- THinay bor bo De $0,))2 %, Mod-#,20 sy shaes wired to Cael vemaindd $ % 24,9243, 44876 “xeq ) 2 TranstherTable* Fill ni cytlicardee Traps Greph oO (0-531. Design FA “predates. Machine & bare 18 Decimal Cmol:3 40 dre Besa us decirhal do 528042793 % Gales wequired oc eacds cemasrele £%)%.9> 4 , @0-34: Design DRA for the Given Language 2. Le gar|nrol Cees la Ans, ive =$e,0,05 35. oo aud § = 30} g- L= a [nrs} oa ns: Poh aatetn} = +20} Bo Le re aie oe Ans. Si M6 9,ab a5, - 3@° O36 Ze sat Ae Le scaby"|n7 0} a Ans Given GLO* O" L = $ &,ababa,-- aa Tegab} 5 L = £a7"|nz0} "OZ Ans'. on Latta. 3 WP Theat > 4a} : q 6- Le aes Eorezo Ars BF atic oh} Ze20} ee yg. Le Zarer|mined rete ee Brea, oryabare’ 2 4abh 8) et ae Fe gate br ny Oo a 2,00 be ve, pes aia stig Me Laneds azbte Fal re --s, abée, Trp0-3 58- Design & OF a which accepls setet shiiee Gran ® oud J's oe el oe exalt eae oP 28 g ° ae Mares-o5] Q36:- Design a DEA Whids anak © cat Zw |WEOIYY, second Syma] xfw) isd deel fost rnp we L Oras O23 Sei Q2F1- Ferthe Siver DrA wile the loyjusy® anal alas giveth? joe Trane ho Teble O20 Ans: ee eee sassy (9-391: Desyan@ DFA ore crt cecepl the Keb op shi pe woth OL rend With ol’.0-40: Design DFA er tne oe Ot an Le Swi Meet, Ww eteby Q> og 4b Be O8" a Nelo) 741, ween) } a 42 gus” a L= SW WIE, wetash} BB eS” ae Le gui ngadrl, nygwd=2)0ets by Ans! oe 4 Con Dab 928 (hos) 4Q-41%- Design & DPA ter the a= sabrw Bw © 3ab7*3 -49:- Design DEA forthe Le Swob eo east Ans: Gwen L= Zab ab, aba, beb pbb, cobb bebQ--- 3 Mean Gata Substne ab Q>b Q2 ir BGO | | (Q-433- Design @ DFA which a ty cep ol Sinus Srecrthat stn * onlay ce aa Delsteia wat paleo aahsutsinng - one " Ans:- Bie evo 4 (i) 6) oO. 0. ! 1% 9) 1 DPA for L Ganferining Stings of O's oul 441 Des Language Q a's whee numba of Os nok devaible oy (AxTD 2018-19] Anse 1 @ oy 2 pra (81 275) 1 F ve BE 3.40)%)%0NEA-Desianlig > Simple Desinnine 2% Compared ts DFA & O-L: Conshutk NFA axeephig. a set of Strivié ott 3a, bf 1 which Cael Shnig af the Lowgtinge Stank with Aw: Find ti ‘for given Gndihon L = abbxxe = abb Cotte Sabb abbs, bb, Abb abb--~f ue $24)b OOK ' (O-2!. Consbuut NFA aceeping-a Lef of. st each sing of the er with’ Nove: No need % Remove Dend Gofgutahe ¢ Dese! Configuiahen allowed men aba watbich Le x tadh = Ca pedtatle =Sarb,cabb bath atbenyy} ab Nie OR ayo M2 Sober Q-B:- Conthuhon ofa NPA aceeptig. @ ket of rigor 30) bF mn Which each Stig atthe Laslage ve Bt Contains Abb ax the Subshiig- re - Ans’) Le xxxabb xxx = Cab) ebb (oth) NEA: ae Ab ME 0466) Q-4! Design Nea for 2° Syamia| Pron HSAs a, Crtaybi Anat. 63 6) a 6s" Lz Cagsacat” Q-5; Designo NFA fr 24 gymbo) from RISA, are Tab Ans. |e (edt a Cath) SEOQ-Gt Design a NFA -br the Longuage |= Cab vabayt Ans. Givey Louguage Le ZE,ababer, abgats, abala,---- 3 Q-F2-Design Na for L= caby teas yaa Poet ag Anse Given L= Cas) "Cba U8 Ly be. ab Nea for) = Se &" Nra forly = AGS2 Now NFA Eg & 5 ssi Thomson Grstraation Ago. caplet? fe will De 1m detain Tern ore eS Q-B:. Find the NFi Lith Pou, Stale for the eo Le sca”: nz0) via: nzLh-Conversien frmen NFA to DPA! An NEA Can have 210,076 or more @ Than one move from a ven state on 0 given impul mbo!: An NEA Can aléo have NOU moved C Moves uuthoul impul Suinto| ON the otter hand ,DFA hel ene. dud Only one move from 0 rven Stat on & ay ven Ini Conversientrom NFA to DFA: . i Suppue there is on NEA N= ( 0,5, 5\4a)F) which reeaginens a Langue Then tte DEA DE ( 05,6", Aq) F!) Car bx Graton tor Lovgune La eps: Initidly G'= Shera: Add Goto G! Shp! Far enh Stats 1» Ql Fine! the Rasible se} of ste es-fer enah input J ustie transthan fenchan 4 NRA ef this bed of cates 18 not mr @) bibte QI Sepa. Find stale of DRA bill by al Sfales with Contaun F (Rratctaleat NPA Byample: Consider the follnoig NFA Shoson th Fig: cS 2366) Ox $m}, E4985, = AME FH 21:3 S:C Tranuhorhachor ePnFA f Steps: Q'=b Sab] Tb opp: G!=$%oh sce » Foreaedy Stabs In Qs Find the each = re ce &' 18 Q find moves inpul Syrnbs] a and, b uding franc | tow Toa uta tod Td tones ale 0A 8! CTromthen archer DFA) 7 a abit toe Considered OS o Berge sil Gate | NDE $ % 21 so b _ ihe As tte is no [* $%2}| % | Qle Pe £0,933Now, Moves from Stab 3 %,%3 on defferent Input Srambols are rot e Vip ronsihéo “tle of DPA, We will oltwlals Jt Like “ mr Pret S'($% 42,0) = 8 (%A)VSC%,9) = F%, Ut 5'C$% 3,5) 8 (jb VTC % 14) = $%,45 Naw we wll updale the tronition table eh DFA 5! CTeamthon Fancher of DAD Stale | @ b = $9023) Yo 3% yf | $40)%d | $20,434, -NOO $4,053 eu be Considered ax a Single stabs Asche eoby it not rn a! ads) st ta slicers FH, LM%HL, 2%/035 Os Nad, move % 4s ” Symbols abe 0} + yo hrokihor able of Dra na a ies ” 5 ($%43,0) = SCH AVS (4,9) = £%/%t 5 (E% Ayr) =SHD)Y EL b= 2%} “Nimo we tail updat: the tramitar fale af DFA S" (Tranather Foncho ohDFA.) oh Q? Gate] @ |b b aa E859 Ans [Ah 2%0/24}| oo 9,233] £43] %0 As there ws no Ned Stats generated, wearcdone uit Cthe Convesien- Final slatiof DFA wiitbs stake blbich hes 9,04 tte Gampenent 4.2 $%,4 2 Felloeoivg Wt the various fatemoters for DEA. OlE £2, $%,21}, 4%, 4} Fe $ £tonu}}, dud Hamthoruachan 5” as sh above +The feel DFA tar above NFA has ben Shon 7QuL5- Convert the ‘llecing NPA ts DEA & Ab 8202-020 Anss- Toansthion table forthe givers NFA B- Transihan Table far DEA Y= [a lb BABE] A BAB k| FACS 34,8} | FAD} SA8h| A from RHE 16 0,OE = 34 byard [Ae Tv 2015-16, Marks-so] 0-24 Design NFA foe a sytol Gmvut t DFA » Ans'- DSA Le Cate) et ea a,b Bie Symeel: m a NFA’ SOS O2CLO Of] | Q/s | @ ‘ 2A | AB} A aes aes ZABCE | FALC3 Arsi- | sajcy [2ABDE | FADE fs A,D} | 24:8} A 248D3} $4,8,c3 | $ajcz FABLE| FA8,c,D2 | $A,c, Dt LA ,CDE| FA) 8, Db [iat HRA} FAG, oD} | 4460} SDT NN 9 8 Oy NOTES 2f D> Su4mbol from RHS 4 O.,over Z= $a,b Theo No.of States m Qrespondiny DPA = 2”® Q-3: Conyert the Polloed ing NEA ts DFA O2G2OLOre Anst- Larguae for the given automa nL. = Abb Casnjrere setet all Shing’ stat wuth abb over Fa Fash a q » taps — ~ “NOTE. only Single Conduhon stat ae With W e2ushin NFA, ith HPs of quesher only add trap stati aud Define rng move “ny NPAWDEA Convers Nothing olse - G.at-corshuit DFA equivalent o NPA where SWS defred ™ eres oe [Ak TD 2015-16,Marteso] b Cc B B Ans. Trusther Title foc DPA, a ws | & b GA | FABy |S ee | tpe [E48 SABE] ZABE [28,04 HBC) A FAB Loy | AGE ey Q-5: Convertthe follearg NFA Anst ine DPA, Whelt yavgiven ba Melo 2 |. =p [2s |t DFA,’ ee [vw [ar ris P Fs ¢ [P| * TAKTD 2018-14, marks 10] ; ‘p # oe) avert in % Transition GrpENEAS JNIFA with &- Moves Ex: L= Sab cK | mn, k204 DE Be © NFA whith & Can be Gmyerted to NEA wulsveel &,Qud this NFA wetrou! Gn be Gnvertel to DFA: te do this, we will use, a metod, Which Gy reumove- QL! the E- transition frem given NEA The method wel! be t+ Find eulall the &-tonihors-from each stole from Q: That vit) be Called A E-closurr(9i), whee Le 6. peng ca ecg ee pn nme Exeloguil(Q2)2 seh ob all Pate Sle ofthe axcmale Cura wut, e-tertton) Which Gan bs Yeashed from i ona path labeled by E ce wusbeuk Gnsuming camp inpisk Syento| ; Bel G-elagsar (40) = $%/%%4 t Ercbegau (%) = 29424 ‘ E-chsu (I) = F223 2.- Ther 6 -pronihens Cay bx abjained “The S!tronayhens meanso. E-closuls 0 a OS moves 5 ayn) = Elem LS (eden), 3- Repeat spo for a> Ly~ Final Stok: en anes 7 ne e-closun (4) Gmtainé ¢ Stake af F mpu Syetel and eash staliaf given NEA j F > Othensdise 5- using the resuliart gales , the transition fable-for equivalent NFA titles B-Co7 ba WillExi+ Convert the -folleoing NFA with Ef NA witauté, 63) > C228 Ans: We Will fret Obtain E-Clatnas of 4,24 0x0 4, 24 fol loeak e-clasiar(Qe) = 2%% Eels (21) = $24 geet (2 E95 “Now the 6" trarkihin on ach Inprk Symbs! wa obtasned 23. 85'(%,2) = C-daguas ( D(E-cLasou (%0),4)) &-chasmr ( 6(2%/4)) = oa "ino see Seman 5" Goyb) = B-classm ( 8(E-Uossst (20), b> mon : = £-ubyt( 8(%,2)) 5"ojt)= 4/213 = Soibd= & Now the Sttancibén on 9 vs ablaiines! 0s: En D= 6 6'(q,0) = Ervlocuu C6 (e-vlowit(%1),0)) Stee $23 Me erclosuat (8 (490, oe? = g -clot(H¢%,0) ¥ 5 C19) SCM b) =F} ; = E-tlesu( po p= the NFA Lanke Shown 5' (Qj) = E-easou ( @ ce-eatoe(2), 6)? tie tone ain = -plosor (60%) ans fe? : g-clasus ( 6(2b)VSCHE)) = E-chsot( Go %) =393 “x “Now 8-francihén on 9, obfodned at: Are: S'(90) = Caclageu ( 5(6-eaCh),2)) & e-closwu( OC Mj) = Erase) 174 1 be Me -cbnswuld(E-vectcA 5) oC ib) Clase O Ub) Elen, ) Now: ths Name. Stee Gy omel 9, Becorne the final shake at £-clasuue of Sard 9 contain The fine! Stali 9. Thee MEAPEx:. Convert the ae Vth € NEA wuphout & Rs Ans: We ee obtain ae 4A, Baud ¢ 2 folleeat E-Clesw (A)! = $A, B,Ck €-cleom(B)! = 3 BCE E-desw (0): = $02 (Naw tee 8 tranattion on cack rnplet Sapmbal ib obtered 2: [elecc | an c Os [E-ctesum | Pe fs @ [ree faa | tet fies | © [22% é LB ch 7 © $03 @ fa) $c3 ee eS 5 (4u,,x) = €-dosun [5 (E-etesa (22, % YJ “Nowd Transi hin Graph ar NA wteltped Ans!- sta A,B and C hetane the Arnel Soke 24 Cclotau of A,B and c -NOTE* wen" Contain the nal Stolk C‘Stepa ir Convertint SEA yuh Ent Dea: & oe oes Jake the E-elacun fr the Starhig Stab af NFA Od a.sharhing State 2 Find te States far each input Sypra) that Gee, trove eon the Preeot That mean the Unie of ration vo aul Ter Cia French Se of NFA reser ji the Cuurseot stati of DFA: 3-44 we-found a ned Stale take wb as Cursert Stats Quel reprakshps. L- Repeat Step 20nd Sep3 Unhi) there 18 no New Stati Rreseot in the Frumthon table of DFA 5 Mark the Stak of DFA as a Aral stil bphith Ooo of NFA. Exomple:- Convert the uA wails G inte be equanvadeed Dra Srb-26 1,6) ee Gl" + 2 cfageat each slat for SHC: Let us Bran € of 3 Cee E ee $504) NF Farin the final stele E-clsSu (9) = E%, y/o = E.chemlgye 2%E Bhen) = eeu scent fcbosuu(, d= fed =o geclesets (IB) 423 the DFA will Echo (ta J= 2 os 0 ‘no Le cS lo) =B PE G3 4 Sy A, Hence nth oye "cla Ct 8 932/OF FE aaah top) 05(% pot x eel a chet ibeastee 8 Aw a Sapp reeaeteens FOC MADT " BB clas Sl Corl DV 5% LY XU toh x E-Closu $74 = ft =B3 nino §'(0)= e-vesms $51, 0= 5 '(Bd) x Eelasat Sy bd} Etats § 9a} = F 20} we gela Convert the Given KFA mto its ejuivaleot DPA. 2 1 2 Q Q Q Solis Lek us obtain the E-closuat =Pench Stal E-Clesu (90) = $40) % 954 E- closwat (%) = $4, 45} E- class (9,)= $9, Now we wil obkatin &'tromshan- Let closet Y= § 0/89, 3 Calla ay sob A 5 (A, 0 Je E-elacosn$ S (4,44 42),0)} = Exlosiu} 5 40,0) (%,0) VSC,0)} (5 Ecclagutit tn = $40,244 5 (Ay) =e -claent $6 (lyf) 1) }eclou GEC DUEL IH ‘nef 2 E-closal $2} =4%, 27 Gllab as shat B & (A 26 claubt $5((% 0494), 2) feel $52 29051 2,230 SCH 2)} 2 b-latun§te? = $%) Gallet stale C ‘ Thus we have obfar L acs Oi(A) =A AD= 8 =o . C ve r eh tite ota z C foreach inpoul- (By 40.) 099 Eeelasou $ 51% 0) VSG DPH=P turd) fi Elan SLORY Df Ereconl > 2)08(% 2 P= E-elacatf Po} yy S00) = E-esans §'CB,1) = é-cbeo FO(C%, = $94} Ce stab Bat S'CB, 2) = Ela 3S 4) DF Esher e ee Stabe C seh an ~ Thus echt Sts Oo) @, 3 (6,L)=8, SCB VES Now wer worl! obfour transition for C: “ e-bous45(0,,0 DEB ak 51(6,0)2 8: a EB O = y FE erase $00, DF oCent) eet zh ; y 2 ehh 5% ,2)$ Ant 82) Sat 2 Ag A= $50j8 92} 0hich ral shal 9, Wes hence fal she. B= 6222 Wh nohiodn the Stale 4, es hence B 18 also inl seke. C = $4, Jothe stab 9, Wes hence C 2b po o fh7-@ Anse Similacto Previous Qushen shat find B-chgut of each Stati. O/s lé-cloum | 2 6 2% 140/949 ,953 | 240A ts dab | £245,403 % [29% toe | LIM trdet | £93,204 4, |% 23 } £45,4ah 4, [tbe | tad ? 4. £%, 90%Minimizalion of DFA: &-NFA—> NFA-> DRA->uinimize DFA @ DEA minimizahon Stars for Converting Q given DPA % 1H i WWhid minmum numbet of Stables «for cout DFA f+ equinier Dr L- Reduce Unveachable Stafi 2- Reduue Equivaled Soli Equialer) sales p and Q, abt equioeet CPB) siete of ay O(AWE|F aed SCAMEF oR, SCP x) GF vd S(HX) EF 4 [xe] 20, Then PRL O- Bauivaleokstals ap ixte br Then PEL als d- Equivalent stols ab [= 2, Thes Pha ot 0+ Equivelest slob a fete 1, ther P&L ane 1) Ejuivaleoh tlt Fito method far minimizahen 2 iri ulbe deen etc oer {- See Partihon method! a: Ny hill -Nerode hearer Gob Pashtion Method: Suppose tare uo. DFA =(O,5,d oF) Which eagnizes toed DPAS (QU Z)8 %, FDO” be Constouhe a Lo Then the minim: Las. . ; ; : us il) inde (sete} soles) mba H00 sols one tet vill Contain 2 ral Stabs as et wt) orth Yn rol Sie “This Paubhon pe Cotled Fe slap’ Joikalice K=t Steps: Find Pr by Partitioning the different Sets of Fret In ese deh of Pg swe mill fake a Possible Poy of States of teo Sales ofa. Sebom bictinguishosle we will glib the Sets ine different A046 1 Fe: Sfep4.: Stop oho” Picz Fey (Ne change yp fatkhon ) steps: AAI Slob shone bet axe merged inf oe. NlovaP stakes I minwnfeee! DFA wil es qqual te ho. of sels m Re Hoo to find wlbather to Stoles 1b Pashion Fe ou clitinguishable ? Tuo stots (4152p ou dashgashatle 1» Pasbion Pea} fer aay mp] 0, B(Qi,0) cund 5 (4p 0) 2010 cefforect> Farhhon Bt ™ ColeExt- Consider the folloding DFA of CAKTO 2016-17, Maree 7-57] @ Sol oShep: % will have eoBed. of sakes one deb il arn 9, Whchaue “fnnal Stakes of DFA aud other Let will Ctayn reas Stated «0 Fe = 33% 9 Fab, 340,43, 952} Shep? Th Caleaak we wil check Ybor, ses of Fathhon fo Car be Posbihoned or not i) For be F%,% 944: S (4,0) = 8% 0)7 9, 42! 8% 1) 8% E95 80% O14 4 HE not cbabnguistable Simila "3 oj0)= 51940)? aed 5%,1) 28M = 5 Be aed 40 rot dishnpurstosle / Since, god Po not olishnpuushatle anol and 94. a-elBo not cba hnpuithesh, po 9, oad "4. ‘uu not ckshguutebesle: BO , “$9, 9s,Aar} Bel mud robe Pasbbeed BD for 844.9919 953: 5 (%,0)= gy aud 5(93,0) = Io S( 90,1) 29 and 8081) =F a aud 43, 001 J 0 ate Gy Ord Yp vespechively winichautir apis faubhin 7 Eig Hows =f % ud FeO Im Sypte Lave yaw be whith ONL” Borne beb 1h Fashhen RB, 60, 4oand 9, cue notes 540) = 95204 51959) 9s and 5(04,1) = 2, and 5195 A= Mover of g, ond 95a pak Syl L 7 ard 45 vaypeatvely whieh On In alifferoch BEM fasbhon fo. $0, 4 aud 95 ne liu hrpuishat le. Bo pset $ %fo,05} wall be fuhhined mb 4/93 Jane £454.80, Re £24994, $%,%34, 4753} To Caobeuleh Fo, we mull cheek whet detef Fashion Pan be Pauhhmed ov not :il) Fo sh 3%, 44,90}: ® 8(%,0) = 5(4, 0) =9,0ud = ditrgeii 7 JaG,oud 51 %,1)= OC W= Ie, £0 Yard 4, au not Suman, 5 (24,0) = 8L94,0) = 9, oud 51 %)1)= antno dihingusbosle P= goed Ay) =SU|) =A, do gpamdt Sime, % ae dishinguishase avd Gyaurd Qa.0xt alae ret oi higut ma Fone a rob clahmpuitable Ao, $24 fa fapaeh Ole ee Nn ru Wy Rr beh 59095}: 5 (40,0) 95 24 51 %50)= 40 O(404)=% ound § (93,1) = 14 Moves of I cud 4 270 ' ] 0 ad, ard Gy vesperhively whith aut in Bae bo pe item, nore ade Sy {ait Q,0nd Qe wthich aut tn Soave Gee tin Pathien B50 49219 not dushinguichasle v) For bed $454: . Since we have only ane slate ww this Bek, ck Care be fut favbhiemed fo, Py $5.9,/4,,04b, erst SH Sint2, Reha this 1b the final Pauhtion. Pashhan B meant that 9 Ap84 ‘Sales om merged mb ame Simi» ad Qgous merged into ane Naw Minimize Det Conrespordvs ts DFA an!Ex:-minimize-the Dra Giver beled: ® @ Sol”. 93 ts Onveochatle shah m giver DFA fo dig ase ch ond corhouk “Fronuthon Table scueg 45 Freviees Quahan find. Py pathhen L for $42, 9 94-95 %6 9 f , x org ened ek § 2 oad Raga ae ity Wad ib Prac Pag 1 (SMPs 8 Process Pax FIR ean ob wu x, G, three Ye Ter Prapleceby 9, nue, vespechivelyEx:- Minimize. DFA Qra for P pai: = [01% } A908 ate oe nama ale AUK) ow Pe! aa 4 2 [aannt, 2] ale PHths3 Zz - We mes Pahor’ Now Pp* — 2 it z HA (% Ae? [teas ttetel ale F ee a fr 73 an * 3 hen 5 seni tne] CRO Ja, b att Pac Po (Sepyé i p doe) ee Lamrd,2n9st4] y, ivolenk stele stele herr 9 %%, oe wid mace Sri § rennetMyhill Nevode Theorem ?- .Minimizahen of DFA @ Steph: Dowd @ table fy oll Pars of Stafes (A,B) Stopa: JMork OU States Pairs Where AEF od B&FORAEF Oud BEF Slope] there aut tus worse Fours (A) Sub thal [5(A,~),5682I] 1 marked Mark (A,B where x64 au imput iprbo) Repeat step, Unb! no mare roaring canbe made Stop. Gmbine Qu the Unmarried Fayre ¢ Equine Sts) and make Them 0 Stigle Stak 1p the minimized DFA Ext 1 feu Drea Tale: 0 eee oO parcuntel de $CA,B)/CDC EOE DIEM core AYR, D¥C, EXC, EXD, ” Nipva Cheek marti Rusite for nna! ee 7 martes Stake Accor fur $ (BA,LPC), 6 ), CED), ACB) sep CBA): O(BM=AL oR 8(6,D=P CAD) FB COAL = (BO): § 0) =EL OR Spek Una teed t 40(BA) ypot martes! Inia Tmo Cpe) rut mertest Ere) =I cena Pt Be 5 oe a ery (eo: scent} oR cnet } n a a, Unma a " “ (p> ste ESET tore es ea ioe AEE fe meet ~ BCA, 028 BANE’ fo (FA) $ oF toh catcorda te shep3 ee aed Sere) wees marked omEquivalent of Hoo Finite Automate: Steps * iclonhty Onuhnlence, mo) he ee 94,9) the transition for input ges Vi defoned bay. Fda, Pf noe P1924) Vg ame SC 45,0)= 9 The. too aulymate ax not equivalest.<) toc ow Fair( 99% Jone +4 Enlermediat Stat ano the otter 18 Pinal Gat. 2- AL inital stab is final stabs 6f one. duutemale, ther in Setonel Qubrmatte. alto inital stab Must be final Stab efor them to be equielout- Ex. | __£ £ _1 Slop bie No nea stab gener Gi fol Ext Findlout wth the ral auctor da 012 epuivlont ? TSE Too Palen att bp “ef both Acceptve Bame Set of Bef Bf Sting’ - A ic ioleot etcording to ahepl fe ee Fh, Bo A and 8 ase rel cpg ret fo % Ans! AFBOperation on Bite Quemate a 1- Onion : @ 2+ Conealenahon 3. Cres Roduck 4 Subbroshon 5 omplemert 6- Roverne Let y= (Br, EF, O1) aud My= (Bs/%, %1F2, 5p) bn two Fie ae My OrG= 3.4, ZF, 62 be orphan i = Qs xQ, 2 £ ao (4 4) 8 linen (8:Cfa), a Peds 4e0,,00r es. dud dino! stabes [Pen ore AEE hacaph te longue ogg 42% 2 if Fe SD hoe eye) [Peranl te Fa}.M avert Lynley) 44M, Fe §cpa)|Peh om Jperank 2 gFedor ieee ond DMM Fe Oe. ya ; Cael Be : Meee? git: Goae 4ABE Oo 3¢,D} erie ee Qe 8x Or= gata ten] = EMe A 05,804 Hae me! se (40). a “Nowe, ext Arutsnrale. M= Mj M9 = Reo S(ca070)= ts can) Our)? eiteh Dc a (AO, b)= (8,49), BL $4d, sven nnopo cnn seat Similan Restee Moved iy sis, engl Sk eel ee ‘ot Hepa oR Even Noofl Cale?! M,OM2 Ther Mean ee Shale 2 fae, re, ADL Case zt Hf Mrz Ther fine) Stabs = LAD} —_— Lu san high ow of 0 ak rat Btn Hoo& Lye $2] 00 ws not a Substyry af 20? 5 CO yep" i EDM) = oO. Uh a= $x] wende wth 01} Mps Bs a * oT VA CoJtulab.’ My XMz5MjUMz, M,-TM4y=2 Ans'- Fret find Compotthenot Automates MOM, Ql OQ? Inthe Stat: of Gropesiheref Autornale WE FAPZ 5 (AP, O)= (3, (A/0),32.(.0)) = B52 S (AP LE COs Ad), Ooh) = LAP I Similasly Defne vestop the mover Cel My +My 27LyDlq, Nesns either 00 nota Subcins OR ends with OL 5 Grol Stated = LAP, 4R,8: Mer? Caren, Ny XM, PANG» Mest 00 td nota Subsiny and ede With OL , Ther Fino) Stokes SAR? Coes! MDa Meant COxd not a saciegion eords iets Of Tor Find stakel = 2 AP, OF Complemeskef DFA & Make Final Stal 79 Final & Nor Firal states Fira! ‘haes Ae : EX! M2 HAR 26%) " sem) gxfoo unsubstor of} 2 gi” Q° . Mp= COQZD, = $e] 2c clo nt ords wath OL / 2 and change Aree avechas Fromapuse of DFA s- Injerc”a 40 Inihja) ond Final afoherte wll deta > Le sey CAap te cletauls m the vegulet Dab ae 3G” uno Femmes |B MTz ® @ Or Z a me Lum) 2 O(ateFe $a,aaahabe,--2 Lose (apoy'a : 294,044)Complemestof NEA? , &) NEA 2 @S6) + naraupspasoneey OO” Len) = $0,29,28,abor £ Lem £64 LOND = & Ey bby by babe But in DFA nog sr" , b . LOM)= $£0,09,, aba, 2 ,Laa= $e, ome Move. Saag NEA, do Entorbwge Fal stat bs Fire tstale jlementae 1, ba,bb, bed" 3 ToM)= bas: ae Lene Lebsabobed 4 ae belied DA a)= LUD to Shab ts nent LenJ= Lin? Jed nen dyn stat 1 Fined stale rs applicable fr D&M Corp) Cyt hala tne Coplerect of the pelo Assume Sz she mayer cen pH shew NN a Lol” Freak fined Lapel” Le iatt 1 * Le sel 2a'-a = £6} Any eT aT Fina Final tele a4 nor Grol tal aud Non Final ni) Stade, This Gncephrer applicable for NA on 4, SomoMove eee in NEA: £6 fr NFA apnpercenteyen Ter corplores! SaExt Lo 5 Xt Lye Zw | ngto) 3 olivisisle by 2.3 = 5 wl] naleaymrod sf oo - 9 2=0,c36tas |7,00) 14 davisyble bys} = $10] nycaymed s=0, wetasy*) Find LyUly , 4 Dla O44 Lily L-y® M,-M> Firat find Composition ef Aulmate Me™; OMzr MAM ONE Oe O1x0o2 FA BPMODE} = $AC, Ab, AE, BC,8D, Cool’ yt 6 nS = peer ee a, eros, (abel: Llp: Meant Nalio) 18 davisible by 2 Or gtd) devecssle by 3 then Aina) Shobes= $ At, AD/ BE, BCE yun cavessile iy 2 and 77,(00)16 de visisle 4s} Lyla: Mean’ Mal then final Stabe = £Act : (ates: Ly-lg: Meant spat) dente by 20 meodut mater by 3 tn fal cob = gap, nes 3 od ad Cased:O%- Hod many different fo. Can bt denigred writ fAxed mtaltede ove = @ Ee $G,b} due numberof Stake 18 tooo Ans. DEA= (fg, 2, 3, 9, FE) ie 3D, 90, % UF be FEO eat $34} lute paneer cuca! ‘o © . © we O [P® har oes | ent / ainda Sienlalt GD) + rind ed + + 16 = 6A _- im Stab ot frxed Then rtulbply Mo of Stabs = 64%2 =128An Se Hew many wai accept 5 y Sto O,, 2 O O® x cee EX ay agin =e), fats Hoo mag aces 8 - oi beateeg trate set 7 How Nore? ¢leno- oPspoka 7 aud 0-174 ee Th Then serie a E ralno-epDFAz "en , Total NEAZ 2.7% C2") hove veSult Bassummg inthe) sfabad fined: tf mibal shale 18 nok,Finite tira wit bout bein Moore O% depends only Presertstats” Represertes| ly 6 tuples =(Q) E62 A, Ad,Hshere Q): Finite setef shoes Zt Up Alphatet SS: tranathan funchoo d:0Kz28 %: Inikial State €O. AL: Finthe Sel ef %p At culpat funhonk O503 Re TFransibar Gap’ By} input a. b Then 7p? ree a a ay gies Lenn) ene weet ent] Then sin m nop at ™M joa Ye, we op teperceon tootsie np Ropwesectel ky G-tuple 2CB,E,5,%, A,r )wvere Q: Finjlesetos. steutes E: Up Alphabel o: fronton turchon 3 axr9B- Q%! tnikelstef, %€8- A! Finke seteol Yp. At Cubgul further SL OKEDA Represestahon'efrsenty me: “TranushorGrop! bh a np-l/pabpal age” “Tasihes Tet he? Teble Bu abinpuk Ab Then ep? srt) (e, 4 tyes :L£0 ie 4 ere] Yp Sng Lens Smee m ne Me,DesignMoore machine’. Oar Consul a moore m/, that tek ‘ 7 a le ef Set af aL sings : ca Po utp or evely ae of ne gateig Ans, Given = iab}, Az $o,2} F a, 40> 0)-"> En) b a fmt ael oe agi BS c op: o Op :00L04 ve 8 ab then'/p & bane! Q-2:. Conta 0 moove"¥%e. thal fates pel op aul Stans ola, Count no-«4 cceuances of Subsine baa Ans: Grver = 4,4), A=co,t) Q-41 Des} mMooee.t, oe ao Mod cD Cp ED-2> BD b af inpul ¢ baa baa Stoles: ABCDBCD Op + 0 ooo of Cubs oecuns: (9-31. Congimto pecrer, nella pep opolt str rAlos ofp mput Onde Cath 10 or Preckuce B otnerrbrhe Produces cl. : A= (4)8<. ) 0-6: Desgn.Moorenle for Ang: Given = Coy) io 1 CMod5 x Remasoden ipo YP 0 “4 Amt 52% rh, Axforhtst omer-o ler) fn - {LoloDesign rent cisotinet: ° 6. Quy Desgn Mealy mere . (6) one's Omplemect of binaty Neumbec. (> Tiaok Grmplemert of brpaty Number C ans: gnckemplnel a4 mul ssa 0. An. >G0 46 ‘ rnpat read from L-£8 8 M5B,) Testament: muted oo ore rnp £0149 £00", ous Noni 18 34 100 hu cage tie te QY% Qn te rong? Ans: BED ant £ by ° reade the npll from cons Fand nape which 0-2: Dg et Pal, abe y+ input ad pet onde 110 Tren oatpet 6 B wy aap fr oh ee © Given ie aN oN "A Ae ZAG Cd 5 L107 ® he Ye. omer o 3:- De mamesty "i. awcepind Me cred en a Oa se gab pond re am tas Fens Ans: pds wth op aa ol obs OL, as of bh0-42. Design Mealy machine. fir Biinaty Addl: & An. Lost L/L o4/t otf oe ro Ii S% 4 d10 246 -" xe Tolo o0/ 0-4. Design realy machme for Birney Gebtra chon Oe ak) ln sheets Ank:- Loft ot/o pe oxo ov/ 4 10024 OWL (2 -td 0 #6. a 2, Spe p=2 1% pe Yo aie 5 Yar 7 Y10 we Vol TRUE ? a Ojp thessum ofthe Preserfaud frevioss br ¢ Ye , the input sequence Gniain an Se Bequene Confarn LO pen erect mpl BEY cy 77 a> Nore of ThereConversion Moore ts Mealy & meals te Moore.ry. : Mecie. Bealy eee Soore bs esky enki te Monestye KS PODraf C Mooveme) = Powerey Cmeaty my.) Ccorete meaty: Let 4= (,5.,5,4%,A,A) by 0 Mere machie-The epuhle machine Can be represented ay 1 "= (O,z, 8; % , ,A")» The output umber ! Con be Obtained at: A'(4,a) = AC8(a,a)) Ex:. Convert the folloo ig maore machine inh tts equivaler] Mealy machine “The Ouivalenk.Meoby machine Cu7 ae Obtained +h fol roe: A (400) = A(Bltofa)) =U) =O h' (0,6) = (51%, #)) = MH I=+ the dr Stabi 9% folleas N (Hae M6 %4) = N% )=0 N (yb) = A (8(2yb))= Medes Hence the tron then toble Partha Mealy machine (an be drawn a4! lorax, a NOTE: in moore to Mi >. " * Ganvoraian Novel staht Zane; aly Machine well be, aa “The Squt a ho ag YoExe Convert the Given Moore. Mackme ti Lis equivcert stealy mathine a oe “Ghe “> Gd % ay Sol”. the. transite) table af ger sore, machine 6 24 -Bllmoe Shot Jp: % 0 %>0 9, 4 \ p70 MP | awe No BX Convert the Gun Moore Machines Its abs vale! steal machin® q oe sheycesgean tthe ven Pot ay qb Ao) oh ae Kp a Anke Are! ( 3 “mn 52 My ”Ia Vg, Y 244 60 Remove mes e'2' i queria oe Qa: Goestt the neem machine rts us Sei pallet aie Angi Feasutheo Table % aMealite Moore 4- @ O-L- Convert the Pllecrig reals, machine info equivalest Meare. machine 1 ENOIE: th meal te moore Grvertie? i ee sates rer IL Whele Ne no-ef Sleharh Meek and i 4 ‘ me Op Symbols 1 ’ Yes 9t ne aed wy CF sla $6 0 vo y> KN Anst-_ Troha Table 4? bo 9 Stepd. Frat Find eat these states whieh hove more than J bubpuds sioee'ated! watt them- “Gpaud 4, aM the Stakes Which have both ouput Dowd alsraled kuin then Geli: Crooks hoo Mates Artreae tees 7-9, tion dts sell cud Qy (sede wilh eutpeet 1) -Strmiloaty for too State wi NR3: (yea Qn moor, Machine wulh ew) ¢ “Pocbtie, oukpuel Will be algouiated to each Stabe pres Tearl mpuFo Tinpurl 7 ee ns as |] Sal sed setae ont | | | bale % 8 40 | %o| Po 92) «0 a Mm) yo fe LL | = 920} Oy a4 ° ‘a | 191 | %e | args. Fill the exhries of next stab using Mealy machine tronnin Hable ddr Iq 7 ree fi teehee nay fi 60 Input L next sats 4g (4, wubneuted 0). far % (bet? youd 211 on inpet 0, neat tal 1%. mil “ar 9 (20h Maced Gy) cab: 995) Srila nek Obhvs (Aap be ifn!a non eer Healy mebine nto equivelest meere-mactine & a 4 Ot B GO? Qe 1 Y% Bde) byes Ans’. Tonsihen Telefe Over Machine Ang o 7H OS Fat ore SATA |O 68 |L /e8 Seber Op : Kd 180 frooetnt | Bo On. fr Lapa | 0-3 2- Gonvatthe fore seal machine 1to equilerttoonntocs ine bh Qo Q> 02 O° SS GES By \ps [%\7 0 90 % \%\ [%\|0 here 433 % 19) (% It o @ 8 4 hi elyne me fat Moore MeebIne Oa: iy ia roger ma ‘ : mi oun ee > ‘] o ea iGDifferexe by _Moow, machine 4- outputoleperds at upon Preseotstate | 2-f mpukchayge, output det charge: 3. More number of stafex aus required 4- “There si beas hordes vopuirerred or Coren Implemertahen - 5. Thuy veal Slet inputs (one lock a output ave! Stab 6 - Syrchanbed Fenershen - 7 bubpect 6 placed 07 Sladen: Be Eauly te dea gf mpat Stony 4h of Sage The, ouput San 3 tud Moore machine: ° TAD 2018-14, Marks 1o] machine, ‘- pupuutcleprcle 7 Fealstals anc set rp o-if inpul change, eukpat also Chases Z- Less numba. of stoke On sequired: There we ore pando copuivernent Pr Crvunil, irre ‘ 5. Thay yeaut faster inp: G- Asyncbronees pubpi gonerahon- re julpel ak placed on tomtom 3 AL ai clpficult toes” n ghee