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BRQCÏ ?]969VLANVa:=QC<!QC<EÎS6PAM\Ñ5QWQCV;:^<\>YÍ:=VaD ND P QCVaD\E&8 ?@Q9_WEM9QÑfBRQC?]969VRAVa:=QS< ¾ ETC,E06U-VD:=A2/W13479VDC,<0?DC-EX-6YÂ >WVDCEWZ[:=A7D\WCE14 S *+RQ 4BRE&D9M=MfEB&VRANA<@]ÈF;[VaQCB&FRAN8;BaE<D\AE&TP?,E!F;:ÂN<\VaVaD9>C:bQSM=BEY698;>CF;E&È¦DW]9?UVY8;E&QNT`FaÑ%QCE&MÔ<WAVRÑ5Fd8aAQSAVa?Ó:=QSF;E<|V;ÎSD969QE E&ÑY<PFaAE&BgVYEU47eQ69Ñ 8a^`:=?@<9>_E&Fb??,aChWQCASF 8;B;È D9h:=²Rc <9cdEUbc&¹hS354YFERegø9ÐàVaf¦E&j Ï7<P4QC_Ô]`:^D\<\E&EY>@8LAN47:=Va<P69:=<98a_W:=>ER<9Ì`>!QC<9<É?,:=VaE&:=ACV;M=B;FdDÈ D9] VR:=A<9:=<]ÈEUD`TPA:=QSFFVaDÆ>CVÍ%:=_WKCQE:=8;<Æ]PEBRA:=Va<É8;:=VaQSFdêf<9 :=F>SA Ï 699 8aELACSB;úS D hÏ AFaÈW<`?U_,TìA QCh MWVa9Q«= aVaUD`²LANV%WBR E°LM^MhSÏ QC48 D9?E!QD9KCEEAC8a_Ù:=>C]PDWQSV :^QS<W8 V;FM=ERVaÑ5QUV V;QCQ<\EA<@BRE&ASM=_&Mf×&QNASÑ BRE&Va D9<WVÃEBgVRE&AM=]`M½ÏE[AV<`_@EAC?B;DUAHÈUVa:=?8aEE&ASFa_V;E&A]UFa:=ÈW<U?UVaD9TÈãQCM\QCÑ5]`8aE&QS8L?ËANVa:=V;QCDP<UAV QNÑfBRE&VaM=D9MEãh9Í4O8;6\:^8aV;:=E<9>A ?,BRQSAS<¦B;V;D98aQS:=<9MëÜE VaV;D9D9EjE D9aET\AS8L_A:=D< ]È&8QÑrQCÑ%8aV;?D9EFdA4O6\BR8aQC:=?<9>@]PQS?69AC<PB;_D9:=QS<9]PERE&ëì8RA_WV;:=:^8;QSE<ÆBRVaBRFãQSVa?@D9]ÈQCD9FaEEHAS__QÏ ÑÃ[ÛAFaFa]`:=<9E>SBRM^:bEAM 8aEHBRACEM^_M·h`:^Í<à8aVa:=D9V;ECE!hfÌPA<9<`:=_VaEU?BRQSQKC<¦ECV;8aÏQS4M#D\BgQCE<WÌPVLAN<\:^:^<\V;EF Va D\°LE ÔRg a«Ø ½H«5 aN QN ´Ñ#SV;ö&D9=E?,ÍACD9B;:bB;D9DÙ:=<9_ÔESERh9ÌPAU<9?@E&FãED9?UQTPÍæE&8VaD9QE ÑVaÌ`D9<9E:=VaFaEE&VBRQCkl<WV;8a^QCM_ÍÎ :=aM=h Mcd:=<9c Fac&V;h`8aÎ 6Pm0BgVYf¦ÏVaD\4EdD\D\EEAC8;E&_FaV ÍQD\ÑE&<VaD9VaE D9ÌÈ<9D\:=EVaEAC_BRQS]`<WQCVa:=8a<WQSVaM7FD9VaQCQ@69A!F;E&>CF :=KSVaD9E&< E FaÈW?UT`QCM`F ê\nUQCA8 <PE&_KSE&V;8aD9ÈEã]PÌPQS<9Fa:=F;Va:ÊT\M^BREãQS]P<¦V;A8a:=QS8Mf3rF:=Fn9hW:=<,Î o¦Aj·>CVaD9:=KSEãE&<@Va8LANF;VL<9AFaV;:=EV;:^QSÎ <UoPÏ VLANT9M=EY>C:=KSE&F%A!Va8a:=]9M=E 3rF pYhWÎ q9hC?jfÍD\E&8aE F pÉ:=FVaD9EãFaÈW?UT`QCM ÍQC88a:=î!V;VahÈ&<Ñ5QCTW8ãÈ@M=ERV;Ñ5D9VhÖE 8aD9:=>CEDWACV_ÖhhPAÎ<Pq_à:=FDPVaAD9M=VHE!h<98aE&E&ÍæF;]PEHFaVLBRANVa:=VaKCE EM^ÑrÈWQCÏ8VacrD9ÑÃEr? ?^ ACB;D9î :=<9VaECD9hWEUA<`?_UACB;? 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(7) Finite Control Current State q. Transition Table. 1. s q L. s q. 1 1 -> s q -> 2 1. s. 2. 6 3. s q R 4 2 . . .. Tape. s. 1. s. 3. s. 4. s. 4. s. 3. s. 2. s. 5. Head. s. 2. s. 2. s. 1. s. 6. ê:=>C698;Eªú747698a:=<9>?,ASBaD\:^<\E?@Q9_WE&MQNÑ#BRQS?@]969VRAV;:^QS<fÏ. s. 5. ?,Í:=ASVaB;DD9É:=<9F;EYÈ¦A?U<PT`_QCBRM=F%QC<\ANFa<P:b_Ë_WE&Ê 8QSP<9M=WÈ¥9V;D9³E ½«b<9ÔQC» <WF;ÒVLDPAANV;MÊ&V;Fd:=<9AÌ> É!FaVLøÍANVaÊE&FH4YÏ ÐÉc<PÏ _ÔE&E_ÍD9E&<ÍEYFaVRAV;EdV;D9E &«È QNÑOA4YÐ Í%E B&AM=MA?ACB;D9:=<9E _?,WQASB;ÍD9D9:=<9E&<E@c<9ÍAF;<PEVa_¶E>CAS8;]9_QCMb69ASQBR]àÑ E_WVaVaD9:=K¦D9E:bE_WD9:=VLE<9ANAS>!]P_EVah`D9VaTWE D9È|E47:=69V;V;8L8aFaAN:=E&<9<9M ÑL>Fah·:=?@VaÍ%:=QSQ9E<_W?@EVLMAN:=>SQT9Ñ#D¦M=ECV BghPQC>SAN?@8a<PQC]\_6\69] VaVLD\ANV;EVaD9:=QCF;E&VLF;<UAEV;:=<WEE&VaM=QNE&Q ?@Ñ aVaEDPD9<¦ANE V;8LFU_WÌ`Í<9Q:=Ñ AVa8;EUVaEUD9@BREQCA<W?@<`Va_Î8;Q9QC_WM;E?,VaMÃQCANAN>S>CMÊ&QS<9Va<9D\E&>ÉV;E&:b8B_WA?@: ÕJFYEE&V;_W8;D9E&:bEA¨<WV@4OA6\M=:=F8a<9:=ÍE&<9Fd>E VaQCBRD\QS8i<9EÏbFaÐÌPVRA<\<WQ:^V;Ñ%VEAE&BRM=QS4OE&?<¦6\V;8aE&8a:=<WQS<9VaM½>@hFAN?AN<P<PAC__ B;D9VaKCD\:=<9AEª8;EC:ØBRÏ1ANQST94<WM=VaD9EE&E<WQSVa8;<9F E&E&?,FHQNÏÑ%AN:=Va4<9D9:=D9E<9EU>VLANKC]`]PAA8;EU8a:ØVãANAT98;QM=ECÑ%Eh`V;EVLD9ANMÊEßC?@E&?@< E&Q9<WVa_WVaQSF E&>CMQNE&hWV;ÑYVaD9D\VaE&ED98EUhÖV;8Lß¦?A<\<\QÔQFa_ÔÍ:=VaE&<Ù:=MQCh<àANVaFD9VLEAA<T\D9MÊES«bASÔhP_L:= aF ]PBRÔQSQC ´Fa<9N:=F;VaPVL:=RQCAN<<¦SVhVaAND9S<PER_²FaÍVR°&A«¹Eª\VaE ½B&«5ANNQM= ÑM :=?,VASVaB;D9D9E :=<9©ªEYSA²RFYW«bANP< R]P9A8;°LVYH aQÑ ° V;V;D9DPEA?@VYASQ9BR_WVaEFM½Ï7QS<,4D\ANE<@47caX 698aA:=<9V>Va:=?,?ASEBa4D\:^<\ANEd<P_U?]9Q98;_WQ9E&_WMh¦6P_ÔBRE&:^KWF :b_WAE<\_E&Íì:=<caVaX D9:=FãANV%ÍÃV;AH:=ÈW?@h9EAM=4 M=QÑÍúF%ï¹6\Óñ FYÒfVaôaQUÏ]\4:ØBgD9Va:=69F%8;:=EFVaVaD9D9EE :=?,AN>CEQÑ A47698a:=<9>?,ASBaD\:^<\EVaDPANV>C69:b_WE&FV;D9EX Z[ :=?]9M=E&?UE&<WVLANVa:=QC<QÑ74O6\8a:=<9>?,ACB;D9:=<9EF%>S:^KSE&<:=<@VaD\:^F]À]È&8Ï ¾ ET19ÕA:=<W21;ÖÁ×C,:[>2,A?BC,-E=-6 A Ô 4?DA?D1ì¿5>W4Ø ¿51AÙÚ13VÛ:=A7D\C,E1 S FaVaVRD\A8aV;E&E@E473r<969QC48a<W:=D9<9ÒEDP>AN47?M^V;69:=AC8a<9B;:=>¦<9D9j1>:=<9Fa?,E&VLFHANACÏ VaÜ B;E&D9FH4h:=<9D\k=E!:^F Í%^ÝÇ E69_FaFaÎD9È Qh¹Í Î Ç ED9h¹AHÎ E&KS8;E&f¦EU8Ï:^F ?4AD9ACB;EFaD9QCVa:=M=<98L69ANEV;<9:=QC3FaÇ:=<V;Ç:^QSV;ÒaQ,<ÆýCj$V;VRD9ADPET9AM=FÍ%E!E&AÙÑ5M=QCM7V8 Í%ßWV;<9QD9QEUÍFaÈW?,< ?UASÇ T`Ba69QCD\M Fa:^È<\AEM=Ç]9:=DÈFdAHA>SKCT`:=E&E&KC8!VE&< ]9e58a:=QS<Æ^ÝT9M=B&E&_ A? Ç 8;VahfQWÑ5ÚÞQCQC8 < f@V;ÑrD9QCAN8a8a<PE&? _E :=Va<D\EêfFa:=VR>SA69Va8aEYE Fd\Î Ïh94Î D9Eh9F;AÈW<P?U_TPÎ QSM^F DPÇAHKSE A<PTP_E&EÚ <Æ AANF;8aFa] E:=>C8;<9Ü E&EH]9_8aEVaFaD9E&8;<WE&VaEEH_ÉF;DPTWACÈ@_WET9FYMbASQBaÑ ß>SAN8LAH<PÈW_ÏfÍ[ D9?@:=VaEQKCTÈQH?@ø9E&E&F<WÏYV7eÔVaQU?,V;AD9M=EM=E&8M=ERTPÑ5VQHø9:=FE&FH>Ch`:=KS8aE&E&<@]98;TWE&È,FaE<¦AV;M=:=ER<9Ñr> V AÎ 8;8aQAÍ<P_AVa<PD9_EAD\ E?AC_Q] KC]PE&QS?:^<WE&<WV;FV Ü VaVaQUQUAV;D9ÚiE8ahW:=:=>SFãD¦3VÇ TWhPÈÎ AUh 8aù :=>SjrD¦ëÜVV;AD98;EY8aQ?ÍACÏB;4D9:=D9<9EE<\ÍER8aø9:=VV;E&?@FYQA KCÇE1Ñ5QCQC<8V;VaD9D9EE VRÇAÇ ]`ÒaECýUhPB;?DPACANB;<9D9>C:=E&<9FECV;hSQ: Ñ F;:^VLVANVa:=FE:=Î <h9FaVRANA<PVa_E ?@A< QKScaX E&FYAV;VQVaVaD\D9EEMb8aA:=Fa>CVDWV;VH:=Ï?@4E&F;D9Va:=E&F ]Va8R4Ah9<9V;F;Q@:^V;:=AQC<< ca:^XiF F;]AND9VQÍVa:=?@<ÆEã:=<Æ4êÑ:=>Cú6\A8a8aEUE!ý9>CÏ:=KC4E&<D\EUANVQC]`VaD9E&8LEAN8;Va:=:=>CQCDW<9V%F QN8;Ñ EÎSE69AC:=B;8aDE_ VRAV;]`Q,ECÏ T\8a4:=<9D9>E!Va?,D9EACB;VLD9AN:=]P<9EEã] DPÑr8aAQCM=?V;F ÍVaQD9]9E&<8;:^hW<W:V Ñf!EKCT9E&Mb8HAChWB;:^ßUV:=FaF ÈW?U:=<@T`F;QCVLM=AF%V;EdAN<PÎ _UÜ DPANAN<PM=_UVÏ7V;D9ÚÜEYD9D\:=EM=EAC_]98;]P:^<WQSV;:^<W:^<\V;F%¶> V;!QªT9A MbACÇ B;ßUÏ9âãFaÈW<,?UA T`öQC^M=NF W:=¯FVL<9ANQS]PVÃE ßA QÑfa69ÍF;D\ERÑ5:^69V;EYM @F;È¦BR?UQS?@T`]9QCM=6\F7VL:=AV V;:=VLQCAN<fßChE&F V;D9ú:=ý!F Ç%FaV;Ç E&]9ÒaýF ?,ASB;D9:=<9EY:=F_W:=FaVa:=<9>S69:=FaD9EH_@TÈB&AN69FaE<9Q &©ªNb^° 47698;:^<\>?ACB;D9:=<9EdBA<_WQUFaQ`Ï *+LÔ. à z9áy}|á9z,{b¢UzIDI~bNzR8~b9{«L {UL zONv 0©8yLvL{Uv}z,y³á9áâw©«½BNyvw zI~bNzIj~bzyNb 9{©âýLvL{Uv}z9L {UL z Nv ¶vw~iy}|~bNy,¡dN{UL

(8) {bÌ Nv}z¡v {Uv} vLy3v z0bz,{UvLzyLv zR«~b9N{ULiy}|~bNyzI~bIz {bNv iµ ·

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(12) Tape symbol read by the head:. State: q1. q3. q2. q2. q3. Halt. L. R. q2. R. q1. L. q2. L. ê:=>C6\8aED74D9E V;8LA<\Fa:=Va:=QC<VRAT9M=EÑrQC8YA!VaD98;E&EF;VLANVaE Ç 6\FaÈ Ç EHAHKCE&8ã?,ACB;D9:=<9ESÏ. T=0. q1. Transition q2. Change the symbol to black.. q1 q2. Change the state to q2.. R. q2 R. Move to the right.. T=1. q2. ê:^>S698aEý74D9EãÌP8aF;VYVa:=?E&FaV;E&]QÑOV;D9E Fa:=?U69MbAV;:=QC<QÑ VaD9E ÇÇ ÒaýQC<AT9MbAN<9ßUVLAN]PECÏ ñ. R.

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