- untt-4 Automation “Intoductton eRe whet ts compertertfon 2 computation Ws a sequence silops, thal car be pe omed by a computer. uA : ; : The. Th 1, tompuctertton has yarige applicctibns th Comprler lesigqn,!' Hes 3 aorttgt etd rrlelt ee no oor ‘ senoroled fo. En ineorg - Bask concept of Automored theo J a ee © alphatet: : denctis cities & oo intl “set of ayrobols : Wz J Long ltl) B= FOrbrG ¥ sli) s $619 BBS tag: vo " ia hing (or) toord over On calphabe = moO finite osidered © Liat of “Ambcls chosen, fro “the Zz. 7 3 Eq: ooollos ol,|,0 are ssejrobols of “the alphabet : se {013. : u , engih % ~Jhe ching cap be degined. aw cymbe ft the chin Wr be a -Ahut then the length ¥ the | the ho of tel , | Sieg 9 N &- denoted bye I. £4 jet “we cole wis & ; @ Eroply | Now Sting : Tg @ sting have no symbol (or) “the tength of” the chit) ® 0, Hen” & ts called Em airing | NULL © gting - “rpalon nis denoted be Gry at _—————tf , 2 , a Vi )conrertonedtfon | 9% Strings: Jet wand v be any ~lwo aes alphabet =. Thee She — Concactenats i apa BA ie certenatisn — v & rs Fg: Dbets us Hello, Aes vz) hort : tol then Uv = Hellowortd,. + colhbamng 9 Orie wet tH brea af 1 A det hawhe . . pinits number 0 lement. & BD iics tage ee PEERS by hla 7 ® iginile_set if a. set heviny nek ‘puancbor "etient| | 4% called | ano “og, % | Vo seogieg’ == fas bry! Languages : ae 6-8 at sto 36, 804,8 , Leng Ae ret ‘=! be an oles and =* be be “Ket % alt stings over =- of tring and Lfz*> ie alle Over = Subsel Jeorlarn in eg: = fa)b3 theo $ Sea) b, ab ba, aa, bb, abay +23 by! sg'sanhs sebbde-4 the 1 =) fayab, ba bb3 “4 | Efntte ... AttomedaFA) Whal fs Fintte audometo. ? A Finite Acetomerta (FAD OY Einee stale Atctometia (FSA) consist ef finite, estes ond a Set Oo transiestions -Tyor one atte = tO Cthothes Stee. A File artormata can be ohvided thto 3, “Fypes. Thy are, Fite cstecte “Automata C DFA) I Del¥rm mise 9. Non. Detesminish finite tals Acctometa.: (NFA) oSA: peterministte Finite state Automata (DFA) : i For > , ¥ Fyom. each input symbol) ig “there & | exact stot AAC om ches “trons 146 fon m each Store | -then fintte axectometen, ts ested “0 he DEA. Eq: eI J > (Py Se Josby | 3 Grates 020? =X, sre = % kMD% ‘ Ae i ee rai boa fo. | Rommel gehen Tom RH Ys Ae ED FES eee -tuple (OQ 2d. 403 e) mhete, 3 c |g sharinite set of stoted Fis a Rinte set Y Tip Syeobo! p> & he Ririal’ tote ” oO poe che Set of: Bipal frotes Pemetion | she — Tarsitron funchdr h Dra clog tec (as OS LW D=P wv, pear aee WS Cv, Wd (dtd 9s 0d Transttton Dibq rar [21] The Transition oli agram osocietted with Ora B&B a anected ara twhoge vertfcers ane the Boles of The edgas & the — gragh ate the Peaingifon A ror one Bree — fo another = tale EQ’ ‘let DRA me (= $4054 9455 > Ez Losby, | % odoF=Sqeyy' © whee, f° Coo >be cleprtect Os 5 664059 =9,,fStop, 12229 db C42 9 b= Vi Thestepore the — -hromnéition chagyram Dra “ts : fpr “the given i 3O-Q=D : ae , WG Transition able: @ The table. twhich Yvepresents ahe list at Trane tion yoo YS or function % % pie ectomata & called *trensPtibn stable oes 9: : pet Dea m= (8= $40,%,545 9,5 =$95b39, Fords F =a) 4 wheie d can be ep) ned a ‘ | BS (40.9 24, > DLUW 2024s 1 SCM b2= 4, 1 | w The transrfion table oy -the. given DFA k | | states a b | | “| | Vo 4% - Y, Go r Vo - 4, | Language accepted bu DEA: es The Sting x f&. Saf) fo be cccepted ee ginite Ghevfe Arefomect if dCYosr O=P fer Some p @ Fi The Collection 6 » acceptect stingsB called — tanqua a. a o" ae accepted ‘avd Sore 7 ated | by Lem). saoewee Socata rage > | Fe, [ems eter Fard chow ents | Problems Related Yo fanquaqe a fe eee ¢ ae tip | @ chek whethey a shi taaner of laccepted (or) NO. by the “eteotog automata? . aabe -w een Aba’ Not ) Solr: : Gitven w = aabe ij Pde aabe) = 03 “2g CURED = d (5 (4120) >bed | zg 6% oO = dC dt% 2 OO = db O%1 20) 2 4, EF ~aabe & aceptel | — |@ rs ~the Shing (i) boa Gi) co ave aceried | (or) net by the above crerto matte ¢ (D GRven w= bAe ee Jd (%0> boas (d 6% 9 #6), 00) = 66400) =

1" 50000, --* 7 conclue & (im % ihe Aad Of al hings Wwelh an -eveh number of ols and tyen? not Wg. r —_— 2Non defermnistic FPnite sttede Auclomata (FAD: Formal Daten NM che nea Ys .cpeapd by P “etuuplécs (8, = 50> Vo» F) rt d yonere a nite ar, fo the Y sek roles o_ & dhe Linke et % fnpudt sumbds G- & the & Znitial gfacte J eb ae finite act sind ctetes.J-9s the “Lranstien function For each fps mol, Jp cthee a4 One Gre mere | transition For eu’! pan , ther dhe > ‘firite BY auslomada B cated NFA.” | yy) 3° fo- | fe a 4 The transition funefion Od (4, Loa) = Vd Psa) 1D J (SP she oPss---Rd,00 =O dl Pp») FRR d can be clef the} os Lanauage .. Accepted by NTA! A Lengua ik) aeepted by NS i | estate to “both F Ond Tim = 1widG,,wmexog] = ¥ | Problemnds related fo Languare crecepsted by NPA: t- Chee whether the ven Ahir ore accepted or Not bi “Hie ona ausometa. ’ Dw, 2aa Ow, -aba~ GW Ww, abae oO nr B& f is . artes } W yet w,= aa rh 8] Coq AD = J (dC40 242 | = dC $40249% 40 ats : 28( Vor BvdlGem Ud C%a7% = $4044 94 5 ULF, %2 4 OP = $96,4, U4 n= 545% $0 ond | he, Qa & accepted , | OD bet us, = aba | S402 abar=d (dC Yor4 > ba) ) oe ee Jd Cf Got, 5 %24> ba) \ = Jd (%, bad v d(% > bad Ud C4) bad —@ la. Now 5 | § C%0> bad = d (d C4056) 5a) = d(4050 = VU054,2%0%oT | Si ndlarty i SCasbay= b CdCarob) 90)” : = 30% sad= 7 ye 3 Now, : bY 22 bD= FC SCV2 br.” = dCb,ad=> 8 C40, aba) = $ Gar, 142 Gv fH r%2 98 = {4% 1,9DE = IDI +9 aba %& accepted, iW) Let Ws =ab bd (%02abd= J (5 C%2a)>) : = db (4 40947%4 >b) = dC Gob UV dl) UV d(Va,b) $440 FU O o $40 4,4 ne F 9903 ~ abe & not accepted tb 4 THM) a. Fen ~lhe banque e exccepted a ~the folte wth acto tm ator d oO - er" ” ye LVeale Pe Tm)= foo, lly. +--+ 3 4 hor 2m, the an Nr & States oO on i ~4e_| 8402983 Tah 4 4, 6 Fy 4 @ | %9%4 $%% Ve | 2443 é $407 $43 | te} w_= 100 ~ 804 > 120) =d (dC qos 1) 500) 2d (8045 rp) | saee = 5 (or00) 05 7° = S3C4200) VA CdC-Y, 9992 ©) | | 5CIe%a Jou SC +P | + dt4q30) ud (432 | © $0045 5 UE HS = §Vo>%s ony 3OF =$4y 444 | 4 100 BD accepted a, (oerLet w= lol j SreRlaaley dd 6 Vo 3"? J (Vo07!0 = =d (402103) ) =d$l§Vo2N 4 201 S6Yo> WU SA 2a) | = dCdC4o20)3 1) vd C4is0)) oo = P4004 312UdCHD Ls = 3 C4210 Ud 6%3 51D - = RVW4 VG oe = 34054, 3NF eo i tol & not Accepted | SHavbing Fin the oad accepted by the i | . Bs ending aba. | | ctuctoma, : | Slodes a » e Ee a | | Vo | F402% % £02428 ee pM [As 448 A013 ins i | Ge fan % $422 VHS t424 / wal 4934 2953 i en be le he aise NEA & ret i 3 (ovo? 28) = 3(5C 0 9) 2% = SCS 40241 32D S3C e000) ¥ 30H 7 ~d(%0>%) yd CVs 3%) = F40> % Vie J OF 2 (444 Fe = aa fs accepted 2 fe.» faa € a WD pep we oP 5 56d ab) 8036402 4 5 C40 7A YE G4 99)9 36D > = § C4058) U6 6 Vorb) a CVor%o) v CW Gy oes ie ab net accepted =W) fet we aba JDL Fo » x60) = d(SC05%) 5 ba) = JC 4 %or 3, bad =dC Vooba) V dCY,> ba) =d Cd (Vo »b) 5%) Vd CIC%,6)50) = 5(@0,%') 9 d(C ),0) =d (wa) Ud (4%. ,4) ud CU, a) = {%o%) v (4) v (hy, 2%) =A%0 0% »V2, Wene oO aba ft = actep fie, aba € Tim) ‘y) rece Let We ACO SCV0 ,accad = did C029), cca) = dkVo% 3 y cea) = dC Vo» Cea) v d(4, aca) = d(dCGor¢)9c@) V dldL% ,¢), 00) = § UV) 34, 08) U d GUY, ta) - SC ola) Vd l4zg5ce) USC, 10) = (hl%0, 0,0) 0 dQ% £),a) VICI 19,0) a (vo »%3 4,0) ud UM 1%y,4,9) Vd ( Ha) = dL Fo 99) Ud l% ,YUd(V3,0) Udy) Ud4,29) ZN AGU $453 U 1350 LF4 UMHSWlet We aaa g(or9a) = d(SC%0>9), 99) = S(L4o2WY aad = (Jorae) vCY, 29D = J (Sl¥o204) Vdd 2% +) . ee Ud AW IH 4.0) . apd a) v Gl, 2%) VdCU | $4504 Fr WH vt 03 i 2 GoW 1% BF A445 +e | ao =&% cxctepted . =< € Tun) Nien We abe $ (Go, AbO = 6 Cd Co 50) 9be) f = dC 440. U 32 bd = d(Yos bd VIL bY = fd (Yb) 0 © §(d CW DO) = I EVV ye) VU one $4,3%>5c) = d(Voodv d(G229 vd lM) = $4024 40 1424 01S Ios 7 ba, TRF = o abc = nol accep Re, abc # THO Design a firtte Autforeyto. fev the coving toni Sofn: pee let DRM 4=$8,5,d, %or™) ” where | ao B= TF. WI, Ve 3 = = fo913 4 Jo & an Trrtal Atele. aad J Can be deghel as, Artotes Oo ' 7: Vo - VY, VY vy, | - We Ve _ The finite Automata = Le — )—— © 3) o “@) @ reid comata > cohPch Occep ts OS te ee st ard ode only Hose Stemg UF+th o. Soln: Gitven L= £ 1o,fOO,\05 loloo,. . - % i DEN Ee a =, Jb. UW) ©) wheie Q= {404,542 3zf0,1k qo an Patital ~<+ate ee {Vad g tan be degre 8, totes \ ® Dasho 9 Berit audometa! te accept “the Ghihg "thet altoays en 00 @ven L= {908,100 » Soe oo loloes oo ave crete Atforectta ts B Desk La iri te cuctomata For -the Vang wae” Le easy? | 815 : © Solon Gir ab, abab » ababab “ The — Fidite nutoreate Es, = Or Gs)= We cetmne{ dean tntte artorctia bey n the a Lega” an 13 a ® Desiqn a cfitite arora tohich accept eld no. 4 & Ne and eal no O's. \ So jd @tiven L= £1/05 bl, 100, Jolly M,....4 i; The FA & | ° , : ! YD ‘ > oO Cy — ] ® detan a cauto mecto Lek As q. % ole fer even po. of 1K ond Solp: GRven Le qoogit, oo, colt, Iolo + +4 << 3G 0 ( ie! ace anal NEA: | eytelne_§ me SE | Theorem: rope \é cStafeme nt For every povelent DFA Siatement- | let L be & leimguceg® ace pred Paes NEA , We can construct an :cs y NEA . Then there ertats & DFA shel “the Game tangueaqe “be digas sta cepts Proag: di. 8xZg_. 28 Let Me (Q,2,4d7407F) be a NFA actepts ila! | ’ 7 BS oR ONE Define M = (8',2's 3!) do's FD BADER, poe 34 ™M hos A Stotes then Mi hae 2 ctherepore 8's $Y), L409 513... C0, G5, L 405 SS peat L Werte sid Oo \ qo > V0) ates comtatns “the ‘ gel Oh cle F & the , lates which st pra} Btote wh NFA. g° + paptne 6) 06 poset . SLs fe a ag) EP re i and only) if $4 U9 Yao 93 924)" SP io Pad BY now we Shoo thet \RB> = Lem we prove by fecloction on the vength tthe toput suing w thet - C49! 402 EPy Pao FA 4 and only i Jo, w) {Pio Pe, 9% Bask step * agp wo 16 4 length oy {w Ban empty Ghing) S CLI, &) = £04 & J (qo.g) - F903 Tod vehon jxteps: that the vesulis & tue For Suppase the ipod Bbtngs of ler th ntor) leas, Now, we poithe ahak the, results tor5 stings length tet waa be ao Siikg — whth x havin length n and Az, Then by focluction assumnplin | dC 4o'5 1a) > d'Ud'C 40290) t : eg as a oe dg CLR a Poa Ta) . 3 ye ; | Sd lip, ops ge - Thus 1 dF (A'9 20D: Ex trashy oe Me] ed (40) xad Se oe Hen a the yesult & Wwe for o1ny length | Of Atrthgs Jems btm t Hence +he prox. ! | Droblems yeletecl 0 conversion J NFA thlo D U Dconstrac & Dra equtwlent Jo “the Give NFA hesa)- sys ye] -M=(£% 09% 35 20519 ods Vosf4, 9D J where g ts eyiven by the +able 4 | States | 9 \ | b> % ls wo, SYN lo I) yet Ora | wwhexe, weg 2. d's Vo, F) oat Be £1 4els LNIs L400 15 \ c p s'- $0513 eo = L404 Wee's FLAIsL409F,53s&tep © . \ dELVoIs OD = dl F%03 > D = 44023 " Bieilarly 3'( £43 D= dC $403.1 £03 ~3'(CwI,19= La) | neo Step © S142 W350):d (4405413 6) = 30 %.0)0d0% 30) = $40, V. 304 = £40395 | bd 'CL%54,3,0)- 1 %2% J] exist dD CLYe> MW Aste Jd CIV02N 351) = dCVorIUdS (491) = RWI OFG0.43 = £40993 “d'C £4 054,350) LIA I| Orise step @ 3'( E43 509» SCAMG.8) ra TLH 3-8 Si mila J 'ryan 2d (14.3.0) T4094 3 | - 5'(£4,I,1) = L%059,) )extst“The -+transttfoo Priacles oO table Jor DFA S2raed [Tend | rat RLV [LGW | C40%] KES ® 04 024,9 othe eqyutva font ® Convert NFA thio (| Stotes ° DFA Jovy the qe NFA ts «us eqewatlent Ora LL arcdes © | red rej [2 crease | cpay | Pd [pv ZIEP, ord | read IBY, DO] ©P4,73let ora om! = (8's 2's d', Vos FD } 6 §rPd.rq30 IT. Ep Lyd, anda. | zee aro | el ® =EbI fone | Jo guia d': a d’? ( (P43, 0) = 3 (LPF 20) : — = ThY3 EF d'(IPV oy- [Pay io | Ai mila de EPID =d (FP3 49 = 4p3 Sr J! (LPsq32 0) = dl 4P24 4,0) = d (P56) U dC456) = {Pov} 0p =FP 3 | “ d'(iP.430) = Lea] exhat Sih lar d '¢LP29I+1) > SCE YING e spy vtr3 =4Psv¥ cs (ir. 4Jo1) = 0% exter Step®: J/(LR arto: J (LP. 5,0) 2 SCP,0)0 S(4,0) 0 dCr,0) = eqs v but=fpq.73 - ah -. 8 (1p, 999, 0) 2 IP v4): cated iri) av SCL) - FCCP.W73,1) 2 dC OdTL V dlr) © £PZu {y3ZusvI ~FP,y,73 | wut The dvansiton table 4ov Pra Stoctes oO ' rp rev) rp3 ye req) Tey * [Ryd Ipq,vJ req KIPW rpg Lead Th < eqrivalent =pFEA For the ger Nera oes a/ 2 TUTORIAL ° For & gree NEA , fird ap equivalent a Lp! . GolP: soln: | yet DEA wee ee | whet@s : P4573} 3 | 6’: agentes Leas ERENT 33 ! 0513 states © vet Aah. Aas APS Be Rar ly | Feet ye dCEPS 0 APSSees ee ag d'(L 9, 13,0) 40 FV01WS FV ' $40,413 Soln: | det Dra’ we (EVE WIE er | Ue § Tq0) > FWI+ T9938 ) 3 2 farb3 | 4 - kh) Joris {1UI, 1 10.35 | | Shortcuk : | Sis 8 | [%) [WW [o> ij | fad Pro) : Ia | Po) Bow) 1%). ag dl: hae A: | S(t, 0) = 3 (£903;0 2195 | tte) | OeNy 8! (T459,bd< F (F405 5) oS" CL 4b b) _ Lo 0VWiJ new = 42% 5 Shepa > a S'(L49.0) 2d C£4,%200= 2V02WS i SLY Dade Lo, Wd exist = tty : to di CLT, bed (£V,4, bd - $UY ee SCENT, b)= LVI eatat Pr Steps: . 6 dB (Lo W3ad-d C£%o9% 4,0) “a =d (%20) Ud (Tra) £43 0 $4043 é = 1% $1409, 0 = D443 eae a i f dg? CL%02V15) = db (4% 9, 356d q * dob) U d(%y 5b) = $49,W3 VFM & ic = {GoW a SEL V0,%1 32b9= \%0 4) extst \é | ica ; ba © Oy gorenhate lw stra ind OMA OFA Ee For each slp cerbol, | For cath 2p Sumbol, tp ctheve ts exactly one \8 “these Bone OY tore Yancitton oom exch Stote syangrion from each Stat) yen sition Fpneton Ke “yang toh Fonction | The sl | | “lo, DEAR’ dIOXT 7S Lror NEA’ dB LF 579 | IFO ipo Q 7 5B -G2® pe--e— | | @ nea % eqoal-to DFA IP the Sense Of : "| { | tangoage acceptar@! . Tobey yoor ongwey. | aheetor®, \ Yes NFA B equa} -ro DFA Jn “the Genae (6 gn < acceptance. —+ ‘For eVery NFA. tve Cao conghoc® an eqwivalant Dra. Eunit. “cuctomata uth |par fon rn NFA wilh €- meyers i4 deg [5 tuple (8,20. VoiF). Uohere, ow a Finite «et of Aicles ae-% 0 Rete act % rps cyrmbols Yo. is a iprhetl — Setodd. cou o det & Final Siofe ) | g2k sthe frounsition chooction $: Ox eh G35 2% E- MOK : inecl by.&-—choso re [2™): : t a Q- Closere CQ)’ % clepttad aé ~the Bet oF 4 | Stobes ‘P. Soh thet, ere & a Palh From a atop labelled as. a a> Thed bh Tt the Get OF ibe loti u ee ° from qd. \e “tial S ® °F asa Sr : 4 Clove Yo) = £%,. 4 '% a ea closwvet4,) ~ 4,4, as AL & clogover qs) « £4, 2. OP rsa al Ys fe clogore Por earch ated ‘ Cree e308 ; &- swan © £122 4, 3.68 -$92,3,4,63 Mi G ~ closore (2) - $253563 f @ —closorecs> = $3563 § -closoretn) ie {hg ie clogorets) = £ B73 @ —closovele) = $67 A clasure(H) = THF 2 AX@ osa jes ave actepted oy vot. | and, ae Properties of _ closere J. % depihed ax, az Ba Cy.G). 2 Ec elocove Cape See Co, wood ~clasore (di ww J (4,29, « “8 le a Nee |) g.q- closore ¢£PiyPax Pn 30e & cclocore CPU Coe ooh Gq -clomove Pn) | Pro blems - velected to hte accepted by NFA | dh |. & - moves + © for nice Shown chek whelleer the Jellourty 3/P KO 2 > € Beso &> * 3h 21 ti oe. gol w Let weo) | we know heck | gcelesvye (4) = €V0, Vi 124 e-clogore CM) = 1 %nV29s & .clacore (Yo? * 1423: av is =Q). . staat (44,2) tr ar I (40): FY0.U. 225 Ha) ae saa oq, G) = ¢, clesove (aid ® pen fax, 6 = & ¢losore C42) 2 TV2 | Giver Weo) | Tien § (40,01 | Now, 3 to) : Y tosorergee (40, 49-2) a & ~closvre Cg € £4059) %2 HO) = & -clogvre (414019 vd(4130) 06 V2)= -closvre C{yoyup ob) = & ~closoye (qn) = 10.4 5 $10.4 0423 | Now, r S$ qo = -clasore cats Cod) i = @, closure (Cd CF Fos, »%y, 4s) 1 2 geclasure (d (Vor) 0d, Nod, 2 ge losdye 6 bUF% 9095 (U1) (i pet war Then gM, wer 8 (qo, &= F045 ow, . \ F qo, 29=q ~Closore (IY. : Eat “1D 25 = ¢~dosore WAM 44929) oh = § —closorel d(4o290d%,2)) ~ : U dF, 0) . €-clo Avve (0 0b uf723) 1 = Gc elodore Cay, I= £% ,A230F 2 AD G~ClosvreCF2) F403 | : an / : : 7 1 De a) ui actepted , | oie) Segngo a te ieee _ |Now, §Co,21%= Galadone | F pet F C40, 8840.41 929 | £5 CH qo). Glo, oy= (5 C861 40D = 4 closure 6 as)! = Gdlosore 6 § 6440/1 24230) ie % -clos vye (9) = & a = Comore Cf (Yo) UC%,2) 0 § (Yor 212 OFF |g, JCV20) 2% no taccoptead ,... |X = & clodore (F¥o4u bvaD ls $l40,0) = 6 - dosorerqod= fi £V0/417923 ea $cao,00) = @ -elesurec¢d'Cqo.9) ta 2G celosvre (d (440.914 3103 s -G-clogore § (0/0? Dd (4120 { Jd 42,0) & | = gclosove (403 U dvs) | 2 4 closore (Vo) = fo, Aa} Ig . ‘ (O0,007.9= %-closvre 5 td g "C0300, 2)) qe aC Closarld (£909 %) 1423, 4 = G.clogore JCI? vd (had) S bv bu S403 0 RT BE 5 . 002, re aclep rect A Ls Niiar | eee as oy ee Se a aie 83) Eeutvalence of NFAY hth and ustihout — & mov as 8 icq, | é af _potoet * >), | Theorem. \ 24 ’ aT i Tye lls oes y ‘NEA wth | mens hen b & accepted by ho ttee kino 4 —troves — 3 | Peooe: BROCE pet M = (8, Z 3d 9409 be @ > NFA loegne MB Nem catthodt G-roevas Fog & ~ NOE AM 1 (8) Ed) Te ,£') wohate ynr $4 {contains the LFth G-moves | ' | ie ee ee closure (Ve fal grote oh Mm 4 F otherwise “mM hee 90 & - move) ant gaa) ( Bj_toduchieo J ond d are Same -dand g we dighe vent ie a be amy OE shat Jia ~ 5 (ed oO Chow xe &) becaude tht aredement ce vot tee Fh |g cqo,4) A403 ard db (40)? E -clogere to) | Baste step: lea too Ate th one. 12,464 JS'C40.00- (40.8) CRY def? of 3") A Bsenne -phot JiCqooxd2d 6? Jor ang | Stang 2% % Jongth £9 | Now we prove the yesuttys For ahing pesume LO & @ ahing of, iergth h Let a = WO Now, we must Khow sthetc % length nat\ 3'(1o, wa = 3 C%e,wWa) 5’ C40 wad = S105 (4, 0),.0) \ = Si tpad C-' dlqo. wr=d’ Ve sw =p) a qer B°L%.0) i » FCap, a Yep = Bera -¢ td (40,0, a> ~ = J CI 4 wa) a S40, ware8 (qo ur) Wente the yesult & toe for OD. \ .FA wath anid Se “piotierns related — to equfvatent® wheat fe raves | t. Constvuet NEA cofiiont Go nae S spor TA wth Qe moves ar ai” Sot + 7 : . uth Reemoc fl NFA , 8, J. FY be an 5 5,82 apt) be am A tofthout ee = MOS. yo find 1" a & checure (40) © 440-43 pre PEGs fo, Foe fae tid. : Yo find 8” Oe wet, . ° . € ge - elepere (46) = Sa0.05 7 Eq © closure cw > FU Lace): &7 closure £10493 § (aed = 3'C4e-0) + $00 d+ is 7, 9, - clesure (C8 (Aer G0)? ge eles (50 940.03.69) : closure ( (40.0) » 5641-09) e eq « closure UF roe: 1g dlosure ( sqezub) | = fe ~clostre (ne) . st . 40.44 , -" ob Mol) oe fg > dlasine e840, 9) 4 dy. olagune (8 E490..9)3 7199 eG -elosue (6149,1) 9 41) 2 str -ebane (80 $903) : = & + dlostne i) : 2. £43 ‘ ot ‘ fay |. : 1eens - ] Ecay = Fear) . eggs onune (80840 8929) + tee clotene CE C1 00)) _ a = close (8) . [i (a0) tiny Stat) + Elan ; fede (eC) | | + fe + lose (£64,199 + & = elesune (41) §u3 ofS = Fay The ranatiten “fable Hey NFA wether! Ee = Teves. my 7 ' 7 stares San | : ‘ 4 i We equivalent yop 5 WFincuL Gee mows te the fen BA with fee meves ty fo eonatiuct NTA atheut Gs moves for wea with ee + mome vw | 8 Gs G i felt, gn MIA ath Ge eves ue, mie (a, Fhe Wr) . Metre Me (eas) 6191) be an NFA wftheut & = moves te gird Ge = closure CA) # $4049 3 have ce ru bP afiner fe -ctasure Cae) & havi ae a a F100 dFte ffhd 8° CSS & - closure (40) + F0,09.90% . G+ closure CH) © TdF fe - clesure (99) * $08 $ cae) = & = clesure (te) > $40.4.498 £ Carte) © fe - closure C1) © £4, .993 8 C%0.%) 2 & 7 closure (%2) = £492 step © . § (40.0) + B(ae-9) . 2 &e closure C5 C8 (Fe, &) 015 = fo- clesure (£0340 492% 00) fe ~chesure (804-6) © 81 YU 8@s,.0) clecure C0 Us vt) ae CV) cles Eran + Start clecuve O86 8640. HI) SL clecuive 766 Te AI) cs olecure (F(a) OS CRN veer.) cheoume CEUUUAD, fe etecuve CUD ‘ Fareed [ Fran + gaa May. { re 8 CEO V0. 6929) eg. - cteserre CE Ye V9 wd -clasure [Ri qerr) US C4270 £(42-99) -clesine (2 bd ae) g, - elasuve C49)sie Oe S Jl = F641 90) = & -clasu vel SCS (17 09) _clasure (SCF % > V2 %20)) g-clogured OV > 0) vd (Ya3 ue) i oo) = & - closure = ~ctasure (4) 7 Now - gic 2d Cw? > q closure (CE C41 2 49219) 2 G-closured GU 7 V23) aD) = & closure Cd (V9! Vv dlV23))) = 4 closure VW Uv 4) = Glo gore CVD Aindlasy ! n 3 (192 = 36192) 2G -clesure ChCHCV1 2 4929) 2 G closure Cd $V12424%5D = @-clagure 646 CUD V SCF 2 023) = &- cto serve 40 V2) = & -clogu re V2)A “The transition 40.6% for NFA _ Step - @ eee $42 209= SCY 290) : =@ — closure (8 08042» @) 0D 2G ~ closure (SCL %I20D = @- closure CY, 00) - & -clogure (4) - % ~ Now g 6%") -3 C4 p01) = G-olosurve (CS C%204) 19 =@closvre (g 4V29) od = ¢-clorvre § C251) : Pa) Eres Simila hy ‘Cq - 5 ©%z2 92D ee = @ Upaure (6C V2 92) = % -Chegure SCV » ) =e __clogere C%2) i 84,32 = $24LW V2 ° penalae Tutovia! a, yq))) eb b 1 Se Solp: - ROY NFA wt G-moves M= (CR323d,Foh) | Degin€ Mi = (&, %54', Yorr? TO Rtad eh q ~ closvre! Jos {G02 Vy OF F b ele “eS 4423 | TO Find ¢': | ETelesure. (0) = 140903 | closure (> = AW ¢, ~ Closure (v2 = 1423 G C02 4 = 4 clodure C9 FY V9 d (015%) = % -clasure CH d= $49 f (427g) = Gi-clotuve Cla? = £423 Step a: Fae 84979 = & eclasure( ded (os sb) | = & - closure Ud CF Vos% 4s 69) = G-cloduve ld (Yo 2b) ud lV, 569) = 6 dare C40 vb oy . = ly ~clgsurve lo) §'(q0sb) ~ 14023 My g’eqne) = Se % 3) ; - » 4 cloguye (S (8 C40 9420 =6-claswe (d($%4, 5a)| = closure (54020 Ud (4,303) | = Fi closurd 6 ¥§ G40. Ge ee v giclasive cq.) [Toads ia5] "Ug 5 b)- 3 C496) rr eg -clesure CI Cd 4436)5b)) ~4- clorsare (6 (4) 569) = §-tlosure (6) iu ica, 2 = Gf CW 2a) d ‘ = G ~tlogure Cg C$. 2G, 220) » = G ~closnre (§ e412) ~ & - rloguve(q,.42) ' = & -clesurelqd Ug closure ch) J Lay» = 4% 5424 > slep3: C220) ef q 9 3a) =G- _ clogure ¢ (étd 6%. 5 6)20D) = G- closure (6 442424) = : ~clostrve(o) (aaa fi cq = =f Cab) yd Ce =G -tlosure [9 Y'CI2.> 8)» b> =§~ —clesure (6 C424 6) =G Clesure C42) C43 95) -492% isis~ The hangitin table fs, , stato asp) £b + \ 5 \ FA | Pape [P44