hadzilacos vassos - intro to theory of computation

8/3/2019 Hadzilacos Vassos - Intro to Theory of Computation

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Kcgzlgz{

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0'8' [LZ[ ;

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12/275

: KDHPZLV 0' PVLIBEBGHVBL[

0'8': Phvzbzbcg ca h {lz

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0';' KHVZL[BHG PVCJ\KZ ba hz ilh{z cgl ca H hgj F b{ bggbzl hgj zdl czdlv b{ gcglepzr) zdlg H F b{ bggbzl' Hi{c)ba H) F hvl jb{zbgkz gcglepzr {lz{) H F 5 F H'

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0': Vlihzbcg{

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8: KDHPZLV 0' PVLIBEBGHVBL[

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23/275

0'4' PLVE\ZHZBCG[ 8 zdl lepzr a|gkzbcg zdlg) b{ zdl lepzr {lz'"Bgj|kzbcg [zlp? Ilz b fl hg hvfbzvhvr ghz|vhi g|eflv) hgj h{{|el zdhz P$b" dcij{> b'l') acvhgr g

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8'6' EHZDLEHZBKHI BGJ\KZBCG 6=

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g . v hgj v 9 g

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Kh{l 8' v 9 g 8' Bg zdb{ kh{l ilz x 5 x hgj v 5 v . 8' Gczl zdhz v 9 g' ]l dhql?b . 8 5 $x g . v" . 8 ^fr bgj|kzbcg drpczdl{b{U

5 x g . $v . 8" ^fr h{{ckbhzbqbzr ca hjjbzbcgU5 x g . v ^flkh|{l x 5 x hgj v 5 v . 8U

h{ }hgzlj' Zd|{) P$b . 8" dcij{ bg zdb{ kh{l'


36/275

64 KDHPZLV 8' BGJ\KZBCG

Kh{l 6' v 5 g 8' Bg zdb{ kh{l ilz x 5 x . 8 hgj v 5 0' Gczl zdhz v 9 g) flkh|{l g 7 0${bgkl g b{ h ghz|vhi g|eflv hgj g 5 0"' ]l dhql?

b . 8 5 $x

g . v" . 8 ^fr bgj|kzbcg drpczdl{b{U

5 x g . $g 8". 8 ^flkh|{l v 5 g 8U5 x g . g5 $x . 8" g5 x g . v ^flkh|{l x 5 x . 8 hgj v 5 0U

h{ }hgzlj' Zd|{) P$b . 8" dcij{ bg zdb{ kh{l h{ }lii'

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5 0' Ilz

x) x)v )v G fl {|kd zdhz e 5 x g . v 5 x g . v) }dlvl v) v 9 g' Zc pvcql zdl |gbx|lgl{{ca zdl x|czblgz hgj vlehbgjlv }l e|{z pvcql zdhz x 5 x hgj v 5 v'

[bgkl x g . v 5 x g . v) bz aciic}{ zdhz

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Pvcpc{bzbcg 8'2 ]l khg |{l hg |gibebzlj {|ppir ca :%klgz hgj =%klgz pc{zhml {zhep{ zcehnl $lthkzir" hgr hec|gz ca pc{zhml zdhz b{ 84 klgz{ cv ecvl'

Pvcca' Ilz P$g" fl zdl pvljbkhzl jlglj h{ aciic}{?

P$g" ? pc{zhml ca lthkzir g klgz{ khg fl ehjl |{bgm cgir :%klgz hgj =%klgz {zhep{

]l }bii |{l bgj|kzbcg zc pvcql zdhz P$g" dcij{ acv hii g 84'Fh{b{? g 5 84' ]l khg |{l cgl :%klgz {zhep hgj z}c =%klgz {zhep{ zc ehnl 84 klgz{ }cvzdca pc{zhml ${bgkl 8 : . 6 = 5 84"'Bgj|kzbcg [zlp? Ilz b fl hg hvfbzvhvr bgzlmlv {|kd zdhz b 84) hgj {|ppc{l zdhz P$b"dcij{) b'l') }l khg ehnl b klgz{ ca pc{zhml |{bgm cgir :%klgz hgj =%klgz {zhep{' Zd|{) zdlvl

hvl n) G {|kd zdhz b 5 : n . = $n b{ zdl g|eflv ca :%klgz {zhep{ hgj b{ zdl g|eflv ca=%klgz {zhep{ |{lj zc ehnl b klgz{ }cvzd ca pc{zhml"' ]l }bii pvcql zdhz P$b . 8" dcij{) b'l')zdhz }l khg ehnl b . 8 klgz{ ca pc{zhml |{bgm cgir :%klgz hgj =%klgz {zhep{' Bg czdlv }cvj{)}l e|{z pvcql zdhz zdlvl hvl n) G {|kd zdhz : n . = 5 b . 8' Zdlvl hvl z}c kh{l{)jlplgjbgm cg }dlzdlv 7 0 cv 5 0'

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Kh{l 6' 5 0' [bgkl b 84) }l dhql : n 84 hgj zdlvlacvl n


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8'6' EHZDLEHZBKHI BGJ\KZBCG ;8

f|z flkh|{l b 84) }l dhql hz ilh{z ql :%klgz {zhep{) }dbkd }l khg zvhjl bg acv zdvll =%klgz{zhep{) hmhbg bgkvlh{bgm zdl zczhi qhi|l ca zdl pc{zhml fr 8'" Ecvl pvlkb{lir) }l dhql?

: n . = 5 : $n


40/275

;6 KDHPZLV 8' BGJ\KZBCG

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41/275

8'6' EHZDLEHZBKHI BGJ\KZBCG ;;

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rc| dhql gcz hivlhjr jcgl {c'Zdl eb{zhnl ibl{ bg c|v |{l ca zdl bgj|kzbcg drpczdl{b{' ]l {hbj zdhz Z b{ h fbghvr zvll }bzd

b gcjl{ hgj zdlvlacvl }l khg hppir zdl bgj|kzbcg drpczdl{b{ P$b" zc kcgki|jl zdhz 7 e6'F|z zdl bgj|kzbcg drpczdl{b{ hppibl{ zc a|ii fbghvr zvll{ }bzd b gcjl{' Z b{ h fbghvr zvll }bzdb gcjl{) f|z b{ bz h a|ii cgl3 [cel zdc|mdz }bii kcgqbgkl rc| zdhz bz b{ gcz zdlvlacvl }l dhjgc vbmdz zc hppir zdl bgj|kzbcg drpczdl{b{ zc bz'

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]l |{l bgj|kzbcg zc pvcql zdhz P$g" dcij{ acv hii g 8'Fh{b{? g 5 8' Zdlvl b{ cgir cgl a|ii fbghvr zvll }bzd cgl gcjl) kcg{b{zbgm ca o|{z zdhz gcjlhgj gc ljml{' Zd|{) P$8" dcij{) h{ }hgzlj'

Bgj|kzbcg [zlp? Ilz b 8 fl hg hvfbzvhvr bgzlmlv) hgj h{{|el zdhz P$b" dcij{> b'l') hgr a|iifbghvr zvll }bzd b gcjl{ dh{ b 8 ljml{' ]l e|{z pvcql zdhz P$b . 8" dcij{ h{ }lii> b'l') zdhzhgr a|ii fbghvr zvll }bzd b . 8 gcjl{ dh{ b ljml{'

Ilz Z fl hg hvfbzvhvr a|ii fbghvr zvll }bzd b . 8 gcjl{' ]l e|{z pvcql zdhz Z dh{ b ljml{'Ilz q fl h ilha ca Z hgj Z fl zdl fbghvr zvll cfzhbglj fr vlecqbgm zdl ilha q avce Z' Z

dh{ b gcjl{ $flkh|{l Z dh{ b . 8 gcjl{ hgj q b{ gcz bg Z") hgj cgl ljml il{{ zdhg Z $flkh|{lzdl ljml kcgglkzbgm q zc bz{ phvlgz b{ gcz bg Z"' ]l dhql?

+ ca ljml{ bg Z 5 $+ ca ljml{ bg Z" . 8 ^h{ hvm|lj hfcqlU

5

$+ ca gcjl{ bg Z" 8. 8 ^fr bgj|kzbcg drpczdl{b{> vlkhii zdhzZ dh{ b gcjl{U

5 + ca gcjl{ bg Z5 b

Zd|{) Z dh{ b ljml{) h{ }hgzlj'

Zdb{ pvcca b{ bgkcvvlkz acv lthkzir zdl {hel vlh{cg }l {h} bg zdl pvlqbc|{ lthepil? ]lhppiblj zdl bgj|kzbcg drpczdl{b{ zc h fbghvr zvll Z zdhz b{ gcz a|ii) }dbil zdl pvljbkhzl}l hvl zvrbgm zc pvcql b{ zhinbgm {plkbkhiir hfc|z a|ii fbghvr zvll{' \gibnl zdl pvlqbc|{lthepil) dc}lqlv) dhvj h{ }l ehr zvr) }l }bii gcz {|kkllj bg gjbgm h kc|gzlvlthepil zc

Pvcpc{bzbcg 8'86' Zdb{ b{ flkh|{l) hizdc|md c|v pvcca }h{ bgkcvvlkz) zdl pvcpc{bzbcg bz{lia b{hkz|hiir zv|l(

Dc} jc }l pvcql bz) zdlg3 ]l khg |{l bgj|kzbcg zc pvcql h {zvcgmlv pvcpc{bzbcg?

Pvcpc{bzbcg 8'8; Acv hgr g 8) h fbghvr zvll }bzd g gcjl{ dh{ g 8 ljml{'Gczbkl zdhz zdb{ pvcpc{bzbcg zhin{ hfc|z hii fbghvr zvll{ $gcz o|{z a|ii cgl{"' Bz b{ lh{r zc qlvbarzdhz zdb{ pvcpc{bzbcg b{ pvcqlj fr zdl bgj|kzbcg hvm|elgz mbqlg hfcql) ecjblj fr {zvbnbgmc|z hii vlalvlgkl{ zc a|ii fbghvr zvll{ hgj vlpihkbgm zdle fr vlalvlgkl{ {bepir zc fbghvr zvll{':

Dhqbgm pvcqlj Pvcpc{bzbcg 8'8;) Pvcpc{bzbcg 8'86 aciic}{ beeljbhzlir) {bgkl h a|ii fbghvr zvllb{ h {plkbhi kh{l ca h fbghvr zvll'

Zdb{ lthepil b{ h {bepil bii|{zvhzbcg ca hg bepcvzhgz hgj {cel}dhz phvhjctbkhi pdl%gcelgcg vlmhvjbgm bgj|kzbql pvcca{' [celzbel{) }dlg }l |{l bgj|kzbcg zc pvcql zdhz hpvljbkhzl P$g" dcij{ acv hii g G) }l {z|efil bg zdl bgj|kzbcg {zlp hgj vlhib{l zdhz bg cvjlvzc pvcql zdhz P$b . 8" dcij{ }l vlhiir gllj zc h{{|el P$b") vhzdlv zdhg P$b") h{ c|v bgj|kzbcgdrpczdl{b{) }dlvl P$g" b{ h {zvcgmlv pvljbkhzl zdhg P$g"'

:H{ hg h{bjl) hg lqlg {zvcgmlv pvcpc{bzbcg dcij{ hgj khg fl pvcqlj bg h {bebihv }hr> zdb{ vlihzbcg{dbpflz}llg zdl g|eflv ca gcjl{ hgj ljml{ hppibl{ zc hii zvll{) }dlzdlv fbghvr cv gcz'


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8';' KCEPILZL BGJ\KZBCG ;=

Ca kc|v{l) zdb{ b{ gcz ilmbzbehzl> ba }l jbj zdb{ }l }c|ij fl |{bgm hg bgkcvvlkz $hgj zdlvlacvl|g{c|gj" bgj|kzbcg pvcca hicgm zdl ibgl{ ca zdl z}c pvlkljbgm lthepil{' Bg {|kd h kh{l)dc}lqlv) bz b{ hjqb{hfil zc zvr |{bgm bgj|kzbcg bg cvjlv zc pvcql zdl {zvcgmlv ahkz zdhz P$g"dcij{ acv hii g

G' Ba }l {|kkllj bg jcbgm {c zdlg) ca kc|v{l) zdl jl{bvlj }lhnlv ahkz

ghelir) zdhz P$g" dcij{ acv hii g G aciic}{ beeljbhzlir' Zdlvl b{ gc m|hvhgzll zdhz }l}bii {|kkllj> hazlv hii) bz b{ pc{{bfil zdhz }l hvl zvrbgm zc pvcql h ahi{l {zhzlelgz) h{ bg zdlpvlqbc|{ lthepil' [celzbel{) dc}lqlv) zdb{ }cvn{ h{ bg zdl k|vvlgz lthepil'

Bz ehr {lle kc|gzlvbgz|bzbql zdhz pvcqbgm h {zvcgmlv {zhzlelgz b{ lh{blv zdhg pvcqbgm h}lhnlv cgl' Zdl hpphvlgz phvhjct b{ vl{ciqlj ba }l zdbgn h ibzzil ecvl khvla|iir hfc|z zdlghz|vl ca bgj|kzbcg pvcca{' Bg zdl bgj|kzbcg {zlp) }l |{l zdl bgj|kzbcg drpczdl{b{ zdhz zdlpvljbkhzl ca bgzlvl{z dcij{ acv b) bg cvjlv zc pvcql zdhz zdl pvljbkhzl ca bgzlvl{z dcij{ acv b . 8'Bz b{ pc{{bfil zdhz) fr {zvlgmzdlgbgm zdl bgj|kzbcg drpczdl{b{) }l mlz zdl ilqlvhml vlx|bvlj zckhvvr c|z zdl bgj|kzbcg {zlp) }dbil h }lhnlv bgj|kzbcg drpczdl{b{ }c|ij gcz hiic} |{ zc jc{c' Lgj ca Lthepil 8'80

8'; Kcepilzl bgj|kzbcg

Bg khvvrbgm c|z zdl bgj|kzbcg {zlp ca hg bgj|kzbql pvcca) }l {celzbel{ jb{kcqlv zdhz zc pvcqlzdhz P$b . 8" dcij{) bz }c|ij fl dlipa|i zc ngc} zdhz P$o" dcij{ acv cgl cv ecvl qhi|l{ ca ozdhz hvl {ehiilv zdhg b . 8) f|z hvl gcz glkl{{hvbir b' Acv lthepil) bz ebmdz fl zdhz zc pvcqlzdhz P$b . 8" dcij{) }l gllj zc |{l zdl ahkz zdhz P$b#6" dcij{) vhzdlv zdhg zdl ahkz zdhz P$b"dcij{'< Cv) }l ebmdz gllj zc |{l zdl ahkz zdhz fczd P$b#6" hgj P$b" dcij' Zdl bgj|kzbcgpvcca{ }l dhql {llg {c ahv) }dbkd hvl fh{lj cg zdl pvbgkbpil ca bgj|kzbcg ${ll [lkzbcg 8'8'6")hvl ca gc dlip b{ {|kd {bz|hzbcg{' Zdlvl b{ h jbfflvlgz zrpl ca bgj|kzbcg pvcca) fh{lj cg zdl

pvbgkbpil ca kcepilzl bgj|kzbcg ${ll [lkzbcg 8'8';") zdhz b{ jl{bmglj zc hjjvl{{ o|{z zdb{ {cvz ca{bz|hzbcg' Zdb{ zrpl ca pvcca b{ khiilj kcepilzl bgj|kzbcg'1

Ilz P$g" fl h pvljbkhzl ca ghz|vhi g|eflv{' H kcepilzl%bgj|kzbcg pvcca ca zdl {zhzlelgzP$g" dcij{ acv hii g G kcg{b{z{ bg pvcqbgm zdl aciic}bgm {zhzlelgz?$" Acv lhkd b G) ba P$o" dcij{ acv hii ghz|vhi g|eflv{ o 9 b zdlg P$b" dcij{ h{ }lii'Zdl h{{|epzbcg) bg $") zdhz P$o" dcij{ acv hii ghz|vhi g|eflv{ o 9 b b{ khiilj zdl bgj|kzbcgdrpczdl{b{' Zd|{) h pvcca fr kcepilzl bgj|kzbcg pvckllj{ h{ aciic}{?

]l ilz b fl hg hvfbzvhvr ghz|vhi g|eflv'

]l h{{|el zdhz P$o" dcij{ acv hii ghz|vhi g|eflv{ o 9 b $bgj|kzbcg drpczdl{b{"'

\{bgm zdl bgj|kzbcg drpczdl{b{) }l pvcql zdhz P$b" dcij{ h{ }lii'


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]dr jcl{ pvcqbgm $" hkz|hiir {dc} zdhz P$g" dcij{ acv hii g G3 Zc {ll zdb{) ilz H^PU flzdl {lz ca ghz|vhi g|eflv{ acv }dbkd zdl pvljbkhzl P b{ zv|l> b'l') H^PU 5 ~g G ? P$g" b{ zv|lu'Pvcqbgm $" elhg{ zdhz }l pvcql zdhz) acv hgr b G) ba lqlvr ghz|vhi g|eflv il{{ zdhg b b{ hglilelgz ca H^PU zdlg b b{ hi{c hg lilelgz ca H^PU' Fr zdl pvbgkbpil ca kcepilzl bgj|kzbcg ${ll

[lkzbcg 8'8';") H^PU b{ h {|plv{lz caG' Fr jlgbzbcg) H^PU b{ h {lz ca ghz|vhi g|eflv{) {c bzb{ hi{c h {|f{lz caG' Dlgkl) H^PU 5 G' Fr zdl jlgbzbcg ca H^PU) zdb{ elhg{ zdhz P$g" dcij{acv lqlvr g G'

8';'8 H {lkcgj acve ca kcepilzl bgj|kzbcg

[celzbel{ kcepilzl bgj|kzbcg pvcca{ zhnl h {cel}dhz jbfflvlgz acve' Bg zdhz acve) zdl pvccazdhz P$g" dcij{ acv hii g G kcg{b{z{ ca z}c {zlp{) h{ bg zdl kh{l ca {bepil bgj|kzbcg?Fh{b{? Pvcql zdhz P$0" b{ zv|l) b'l') zdhz zdl pvljbkhzl P$g" dcij{ acv g 5 0'

Bgj|kzbcg [zlp? Pvcql zdhz) acv lhkd ghz|vhi g|eflv b 7 0) ba P$o" dcij{ acv hii ghz|vhi

g|eflv{ o 9 b zdlg P$b" dcij{ h{ }lii'Zdl {lkcgj acve ca kcepilzl bgj|kzbcg {lle{ zc jbfflv avce zdl pvlqbc|{ acve) bg zdhz bz

dh{ hg ltpibkbz fh{b{ kh{l) acv g 5 0' H{ }l {h} bg c|v jb{k|{{bcg ca zdl jbfflvlgkl flz}llg zdlpvbgkbpil{ ca ${bepil" bgj|kzbcg hgj kcepilzl bgj|kzbcg ${ll phml 84) [lkzbcg 8'8';") zdl kh{lg 5 0 b{ bepibkbz bg $"' Fczd acve{ ca kcepilzl bgj|kzbcg pvcql zdhz P$g" dcij{ acv hii g G']l khg |{l }dbkdlqlv b{ ecvl kcgqlgblgz acv zdl {plkbk pvljbkhzl P$g" ca bgzlvl{z'

[plhnbgm bg mlglvhi zlve{) bgj|kzbcg ilz{ |{ pvcql zdhz h klvzhbg vl{|iz dcij{ acv hii g|eflv{)fr pvcqbgm zdhz

$b" bz dcij{ acv klvzhbg {bepil{z g|eflv{) hgj

$bb" bz dcij{ acv ecvl kcepilt g|eflv{) ba bz dcij{ acv {bepilv cgl{'

Bg ehgr bg{zhgkl{) {bepil{z o|{z elhg{ {ehiil{z b'l') 0 cv {cel czdlv {bgmil fh{b{ kh{l'Zdlvl hvl bg{zhgkl{) dc}lqlv) }dlvl zdl elhgbgm ca {bepil{z b{ jbfflvlgz) hgj zdlvl hvl{lqlvhi {bepil{z g|eflv{ zdhz khg fl zvlhzlj zcmlzdlv h{ h {bgmil {plkbhi kh{l' Bg {|kdbg{zhgkl{) zdl v{z acve ca kcepilzl bgj|kzbcg ilhj{ zc ecvl ghz|vhi hgj ecvl lilmhgz pvcca{'$[ll Lthepil 8'88'"

8';'6 Fh{l{ czdlv zdhg lvc

H{ }bzd {bepil bgj|kzbcg) {celzbel{ }l gllj zc pvcql zdhz h pvljbkhzl dcij{) gcz acv hii ghz|vhi

g|eflv{) f|z acv hii ghz|vhi g|eflv{ mvlhzlv zdhg cv lx|hi zc {cel kcg{zhgz) {hr k' ]l khgpvcql {|kd h {zhzlelgz |{bgm qhvbhgz{ ca kcepilzl bgj|kzbcg'

Zdl qhvbhgz ca zdl v{z acve ca kcepilzl bgj|kzbcg kcg{b{z{ bg pvcqbgm zdl aciic}bgm {zhzl%elgz?

$" Acv lhkd b G {|kd zdhz b k) ba P$o" dcij{ acv hii ghz|vhi g|eflv{ o {|kd zdhz k o 9 bzdlg P$b" dcij{ h{ }lii'


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8';' KCEPILZL BGJ\KZBCG ;2

Zdb{ pvcql{ zdhz P$g" dcij{ acv hii g k' $]dr3"Zdl qhvbhgz ca zdl {lkcgj avce ca kcepilzl bgj|kzbcg kcg{b{z{ ca zdl aciic}bgm z}c {zlp{?

Fh{b{? Pvcql zdhz P$k" b{ zv|l'

Bgj|kzbcg [zlp? Pvcql zdhz) acv lhkd ghz|vhi g|eflv b 7 k) ba P$o" dcij{ acv hii ghz|vhig|eflv{ o {|kd zdhz k o 9 b zdlg P$b" dcij{ h{ }lii'Zdb{) zcc) pvcql{ zdhz P$g" dcij{ acv hii g k' $]dr3"

8';'; Lthepil{

Lthepil 8'88 Hg ltkliilgz bii|{zvhzbcg ca kcepilzl bgj|kzbcg b{ hffcvjlj fr zdl pvcca ca ha|gjhelgzhi vl{|iz bg g|eflv zdlcvr? lqlvr ghz|vhi g|eflv zdhz b{ mvlhzlv zdhg cv lx|hi zc 6khg fl }vbzzlg h{ zdl pvcj|kz ca pvbel g|eflv{'

Abv{z }l gllj zc vlkhii {cel jlgbzbcg{' Ba g) e hvl bgzlmlv{) }l {hr zdhz g b{ jbqb{bfil

fr e ba zdl jbqb{bcg ca g fr e dh{ gc vlehbgjlv) b'l') ba g#e b{ hg bgzlmlv' Hg bgzlmlv gb{ pvbel ba g 6 hgj zdl cgir pc{bzbql bgzlmlv{ zdhz jbqbjl g hvl 8 hgj bz{lia'= H pvbel

ahkzcvb{hzbcg ca h ghz|vhi g|eflv g b{ h {lx|lgkl ca pvbel{ }dc{l pvcj|kz b{ g' Gczbkl zdhzh pvbel ahkzcvb{hzbcg) flbgm h {lx|lgkl ehr kcgzhbg zdl {hel $pvbel" g|eflv vlplhzljir' Acvlthepil) ;) 6) 6) =) ; b{ h pvbel ahkzcvb{hzbcg ca 6


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:0 KDHPZLV 8' BGJ\KZBCG

Zdlvlacvl) P$g" dcij{ acv hii g 6'

Gczbkl zdhz zdlvl b{ gc cfqbc|{ }hr bg }dbkd }l kc|ij dhql jcgl zdb{ pvcca fr |{bgm {bepilbgj|kzbcg) h{ cppc{lj zc kcepilzl bgj|kzbcg' O|{z ngc}bgm zdl pvbel ahkzcvb{hzbcg ca b mbql{

|{ hf{ci|zlir gc ki|l hfc|z dc} zc gj h pvbel ahkzcvb{hzbcg cab . 8' Dc}lqlv) ba }l ngc} zdlahkzcvb{hzbcg ca hii g|eflv{ il{{ zdhg b) zdlg }l khg lh{bir gj h pvbel ahkzcvb{hzbcg ca b? ba bb{ pvbel) zdlg bz b{ bz{ c}g pvbel ahkzcvb{hzbcg) hgj }l hvl jcgl> ba b b{ gcz pvbel) zdlg }l khgmlz h pvbel ahkzcvb{hzbcg ca b fr kcgkhzlghzbgm zdl pvbel ahkzcvb{hzbcg{ ca z}c ahkzcv{ $}dbkdhvl {ehiilv zdhg b hgj zdlvlacvl }dc{l pvbel ahkzcvb{hzbcg }l ngc} fr bgj|kzbcg drpczdl{b{"'

Hi{c gczbkl dc} kcgqlgblgz }h{ zdl |{l ca zdl v{z acve ca kcepilzl bgj|kzbcg $zdl cgl}bzd gc ltpibkbz fh{b{" bg zdb{ pvcca' Zdl vlh{cg b{ zdhz zdlvl hvl hkz|hiir bggbzlir ehgr{bepil{z g|eflv{ h{ ahv h{ pvbel ahkzcvb{hzbcg{ mc? Lqlvr pvbel g|eflv dh{ h zvbqbhi pvbelahkzcvb{hzbcg) ghelir bz{lia' Zd|{) zdlvl b{ gczdbgm {plkbhi hfc|z zdl fh{b{ kh{l ca g 5 6> zdlhvm|elgz |{lj zc pvcql zdhz P$6" dcij{ b{ hi{c |{lj zc pvcql zdhz P$e" dcij{ acv lqlvr pvbelg|eflv e' Bz b{ ecvl {|kkbgkz hgj lilmhgz zc zvlhz hii zdl{l kh{l{ hz cgkl) h{ bg zdl pvlkljbgmpvcca'

Zdlvl b{ hkz|hiir ecvl zc pvbel ahkzcvb{hzbcg{ ca ghz|vhi g|eflv{ zdhg Pvcpc{bzbcg 8'8:{zhzl{' Ecvl {plkbkhiir) gcz cgir jcl{ lqlvr ghz|vhi g|eflv g 6 dhql h pvbel ahkzcvb{h%zbcg) f|z zdl ahkzcvb{hzbcg b{ l{{lgzbhiir |gbx|l |p zc plve|zbgm zdl pvbel g|eflv{ bg zdl{lx|lgkl' Zdhz b{) ba z}c {lx|lgkl{ hvl pvbel ahkzcvb{hzbcg{ ca zdl {hel g|eflv) zdlg zdlrhvl plve|zhzbcg{ ca lhkd czdlv' Pvcqbgm zdl |gbx|lgl{{ ca pvbel ahkzcvb{hzbcg{ hi{c bgqciql{kcepilzl bgj|kzbcg) f|z vlx|bvl{ h al} fh{bk vl{|iz{ hfc|z g|eflv zdlcvr) hgj {c }l }bii gczpvcql zdb{ ahkz bg zdb{ kc|v{l'

Fr zdl }hr) bg qbl} ca zdb{) }l khg {ll }dr 8 {dc|ij gcz fl kcg{bjlvlj h{ h pvbel g|eflv'Ba bz }lvl) pvbel ahkzcvb{hzbcg }c|ij gcz fl |gbx|l $|p zc vlcvjlvbgm ca zdl ahkzcv{"' Hgr pvbel

ahkzcvb{hzbcg ca h g|eflv kc|ij fl ltzlgjlj fr bgzvcj|kbgm hg hvfbzvhvr g|eflv ca 8{ bg zdl{lx|lgkl' Zdb{ }c|ij gcz hfflkz zdl pvcj|kz ca zdl g|eflv{ bg zdl {lx|lgkl) f|z }c|ij vl{|izbg h {lx|lgkl zdhz b{ gcz h plve|zhzbcg ca zdl cvbmbghi cgl' ]l kc|ij hiic} 8 zc fl h pvbel)zd|{ {ibmdzir {bepibarbgm zdl jlgbzbcg ca pvbehibzr) hz zdl ltplg{l ca kcepibkhzbgm zdl {lg{lbg }dbkd h pvbel ahkzcvb{hzbcg b{ |gbx|l' Bz z|vg{ c|z zdhz jcbgm {c b{ gcz h mccj zvhjlcff) hgjzdb{ b{ zdl vlh{cg zdhz 8 b{ fr jlgbzbcg gcz pvbel' Lgj ca Lthepil 8'88

Lthepil 8'86 ]l vlpvcql Pvcpc{bzbcg 8'2 ${ll Lthepil 8'=" |{bgm kcepilzl bgj|kzbcg'

Hizlvghzbql pvcca ca Pvcpc{bzbcg 8'2' Ilz P$g" fl zdl pvljbkhzl jlglj h{ aciic}{?

P$g" ? pc{zhml ca lthkzir g klgz{ khg fl ehjl |{bgm cgir :%klgz hgj =%klgz {zhep{

]l }bii |{l kcepilzl bgj|kzbcg zc pvcql zdhz P$g" dcij{ acv hii g 84'Ilz b fl hg hvfbzvhvr bgzlmlv {|kd zdhz b 84) hgj h{{|el zdhz P$o" dcij{ acv hii o {|kd

zdhz 84 o 9 b' ]l }bii pvcql zdhz P$b" dcij{ h{ }lii'Kh{l 8' 84 b 68' ]l khg ehnl pc{zhml acv


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8';' KCEPILZL BGJ\KZBCG :8

84 klgz{ |{bgm cgl :%klgz {zhep hgj z}c =%klgz {zhep{ $84 5 8 : . 6 ="> 82 klgz{ |{bgm zdvll :%klgz {zhep hgj cgl =%klgz {zhep{ $82 5 ; : . 8 ="> 60 klgz{ |{bgm ql :%klgz {zhep{ $60 5 < :"> 68 klgz{ |{bgm zdvll =%klgz {zhep{ $68 5 ; ="'

Zd|{) P$b" dcij{ acv 84 b 68'Kh{l 6' b 66' Ilz o 5 b :' Zd|{) 84 o 9 b hgj zdlvlacvl) fr bgj|kzbcg drpczdl{b{)P$o" dcij{' Zdb{ elhg{ zdhz zdlvl hvl n) G {|kd zdhz o 5 : n . = ' Ilz n 5 n . 8 hgj 5 ' ]l dhql?

: n . = 5 : $n . 8" . = ^fr jlgbzbcg ca n hgj U5 : n . = . :5 o . : ^fr bgj|kzbcg drpczdl{b{U

5 b

Zd|{) P$b" dcij{ bg zdb{ kh{l) h{ }lii'

Zd|{) bg fczd kh{l{ P$b" dcij{) h{ }hgzlj'

Lgj ca Lthepil 8'86

Lthepil 8'8; Ba rc| jvh} h al} a|ii fbghvr zvll{) rc| ehr gczbkl zdhz lhkd dh{ hg cjjg|eflv ca gcjl{ hgj rc| ehr {|{plkz zdhz zdb{ b{ zv|l acv hii a|ii fbghvr zvll{' Rc| ehr

zdlvlacvl acve|ihzl zdl aciic}bgm

Kcgolkz|vl 8'8< Acv hgr pc{bzbql bgzlmlv g) ba h a|ii fbghvr zvll dh{ g gcjl{ zdlg g b{ cjj'

Bgj|kzbcg b{ h ghz|vhi elzdcj zc zvr |{bgm bg cvjlv zc pvcql zdb{ kcgolkz|vl' C|v hzzlepz{zc pvcql zdbgm{ hfc|z a|ii fbghvr zvll{ |{bgm {bepil bgj|kzbcg $vlkhii Lthepil{ 8'2 hgj 8'80"}lvl avh|mdz }bzd jbk|izbl{' Zdl fh{bk pvcfile }h{ zdhz zdl vlecqhi ca h ilha avce h a|iifbghvr zvll rblij{ h fbghvr zvll }bzd cgl il{{ gcjl }dbkd) dc}lqlv) b{ gcz a|ii hgj) zdlvlacvl)zc }dbkd }l khggcz hppir zdl bgj|kzbcg drpczdl{b{'

Bg zdl kh{l ca Kcgolkz|vl 8'8


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{|fzvll vcczlj hz cgl ca zdl kdbijvlg ca Z{ vccz' Acv lthepil) zdl zvll bg Abm|vl 8'8$f" dh{zdvll {|fzvll{? cgl kcgzhbg{ gcjl{ 6) < hgj 1> cgl kcgzhbg{ o|{z gcjl ;> hgj cgl kcgzhbg{ gcjl{:) =) 4 hgj 2'

Zd|{) zvll{ dhql hg bgzlvl{zbgm vlk|v{bql {zv|kz|vl? Zdl {|fzvll{ ca h zvll hvl {ehiilv zvll{)

}dbkd khg fl a|vzdlv jlkcepc{lj bgzc rlz {ehiilv zvll{) hgj zdb{ jlkcepc{bzbcg pvckl{{ khgkcgzbg|l vlk|v{bqlir |gzbi }l dhql hvvbqlj hz zdl {ehiil{z pc{{bfil zvll{' $Jlplgjbgm cg }dhzbz b{ }l hvl zvrbgm zc pvcql hfc|z zvll{) zdl {ehiil{z pc{{bfil zvll{ ehr fl zvll{ }bzd o|{zcgl gcjl) zvll{ }bzd gc gcjl{) cv {cel czdlv fh{b{ kh{l'" Zd|{) bz b{ ghz|vhi zc pvcql zdbgm{hfc|z zvll{ bgj|kzbqlir fr hppirbgm zdl bgj|kzbql drpczdl{b{ zc {|fzvll{) hgj |{bgm zdb{ zcpvcql zdhz zdl jl{bvlj pvcplvzr dcij{ acv zdl lgzbvl zvll' Bg mlglvhi) zdb{ b{ hg hppibkhzbcg cakcepilzl bgj|kzbcg) {bgkl zdl {|fzvll{ hvl {ehiilv ${hr) bg g|eflv ca gcjl{" zdhg zdl zvll)f|z zdlr hvl gcz glkl{{hvbir {ehiilv fr cgl'

Bz b{ lh{r zc {ll zdhz ba }l hppir zdl jlkcepc{bzbcg jl{kvbflj hfcql zc fbghvr zvll{) zdlvl{|izbgm {|fzvll{ hvl zdle{liql{ fbghvr' [bebihvir) ba }l hppir bz zc a|ii fbghvr zvll{) zdl

vl{|izbgm {|fzvll{ hvl zdle{liql{ a|ii fbghvr zvll{' Zd|{) }l khg |{l zdb{ bjlh zc pvcql bgj|k%zbqlir zdbgm{ hfc|z fbghvr zvll{ cv hfc|z a|ii fbghvr zvll{' ]l }bii bii|{zvhzl zdb{ fr pvcqbgmzdl hfcql kcgolkz|vl'

Pvcca ca Kcgolkz|vl 8'8 fr zdl bgj|kzbcg drpczdl{b{) P$b8" hgj P$b6" dcij' Zd|{) b8 hgj b6 hvl cjjg|eflv{' Fr $8'


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8';' KCEPILZL BGJ\KZBCG :;

8';': Pbzahii{

Bg hjjbzbcg zc zdl pvcfile{ }l jb{k|{{lj [lkzbcg 8'6'; $b'l') cebzzbgm zdl fh{b{ kh{l cv bghj%qlvzlgzir {zvlgmzdlgbgm zdl bgj|kzbcg drpczdl{b{ bg zdl bgj|kzbcg {zlp") bg kcepilzl bgj|kzbcg

pvcca{ }l e|{z }hzkd c|z acv hgczdlv pvcfile' [|ppc{l }l hvl |{bgm kcepilzl bgj|kzbcg zcpvcql zdhz P$g" dcij{ acv hii bgzlmlv{ g k) }dlvl k G b{ {cel kcg{zhgz' Bg zdl bgj|kzbcg{zlp ca zdb{ pvcca }l kcg{bjlv hg hvfbzvhvr ghz|vhi g|eflv b) hgj }l pvcql zdhz P$b" dcij{h{{|ebgm zdhz P$o" dcij{ acv hii bgzlmlv{ o bg zdl bgzlvqhi k o 9 b' Zd|{) ba zdl hvm|elgzzdhz P$b" dcij{ |{l{ zdl ahkz zdhz P$o" dcij{) }l e|{z fl khvla|i zc lg{|vl zdhz fczd $h" o k)hgj $f" o 9 b' Ba gcz) zdlg }l dhql gc vbmdz zc h{{|el zdhz P$o" dcij{ h{ phvz ca zdl bgj|kzbcgdrpczdl{b{'

Bz b{ vlx|bvlelgz{ $h" hgj $f" zdhz jbkzhzl acv }dbkd qhi|l{ ca g }l e|{z pvcql zdhz zdlpvljbkhzl P$g" dcij{ }bzd gc vlkc|v{l zc zdl bgj|kzbcg drpczdl{b{ b'l') }dhz {dc|ij fl zdlfh{b{ kh{l{ ca zdl bgj|kzbcg pvcca' Zc bii|{zvhzl zdb{ pcbgz) {|ppc{l zdhz }l }b{d zc pvcqlzdhz P$g" dcij{ acv hii g

84) hgj bg zdl bgj|kzbcg {zlp ca zdb{ pvcca }l hvl zvrbgm zc pvcql

zdhz P$b" dcij{ |{bgm) h{ zdl bgj|kzbcg drpczdl{b{) zdhz P$b :" dcij{) }dlvl b 84' Cakc|v{l) b : 9 b) {c $f" b{ h|zcehzbkhiir {hzb{lj' Flkh|{l ca vlx|bvlelgz $h") dc}lqlv) }lkhg |{l zdl bgj|kzbcg drpczdl{b{ P$b :" cgir ba b : 84> b'l') cgir ba b 66' Zdb{ elhg{zdhz zdb{ bgj|kzbcg {zlp b{ qhibj cgir ba b 66) hgj {|mml{z{ zdhz zdl zv|zd ca P$84") P$82")P$60" hgj P$68" {dc|ij fl dhgjilj {lphvhzlir) }bzdc|z vlkc|v{l zc zdl bgj|kzbcg drpczdl{b{'Bg ahkz) }l dhql hivlhjr {llg hg bg{zhgkl o|{z ibnl zdb{ bg Lthepil 8'86' Rc| {dc|ij vlqbl}zdl pvcca bg zdhz lthepil hgj ehnl {|vl rc| |gjlv{zhgj }dr zdl pvcca }c|ij fl bgkcepilzlba }l dhj cgir pvcqlj zdhz P$84" dcij{ bg Kh{l 8'

Gc} }l kcg{bjlv h {bz|hzbcg }dlvl bz b{ zdl {hzb{ahkzbcg ca vlx|bvlelgz $f" zdhz bepc{l{vl{zvbkzbcg{ cg zdl qhi|l{ ca b acv }dbkd zdl bgj|kzbcg {zlp khg fl khvvblj c|z' [|ppc{l zdhz}l }b{d zc pvcql zdhz P$g" dcij{ acv hii g

0) hgj bg zdl bgj|kzbcg {zlp }l hvl zvrbgm zc

pvcql zdhz P$b" dcij{ |{bgm) h{ zdl bgj|kzbcg drpczdl{b{) zdhz P$ b.86 " dcij{) }dlvl b 0' Bzz|vg{ c|z zdhz b.8

6 9 b) acv hii b ;> dc}lqlv) b.8

6 b) acv 0 b 9 ;' Zdb{ elhg{ zdhz zdl

bgj|kzbcg {zlp bg {|kd h pvcca b{ qhibj cgir ba b ;) hgj {|mml{z{ zdhz zdl zv|zd ca P$0") P$8"hgj P$6" e|{z fl dhgjilj {lphvhzlir) }bzd gc vlkc|v{l zc zdl bgj|kzbcg drpczdl{b{'


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:: KDHPZLV 8' BGJ\KZBCG

Ltlvkb{l{

8' Jl{kvbfl h {lz H zdhz {hzb{l{ pvcplvzbl{ $b" hgj $bb" ca zdl bgj|kzbcg pvbgkbpil ${ll [lk%zbcg 8'8'6) phml 8=" hgj b{ h pvcplv {|plv{lz caG'

6' ]dlg }l jc hg bgj|kzbcg pvcca) b{ bz glkl{{hvr zc pvcql zdl fh{b{ flacvl }l pvcql zdlBgj|kzbcg [zlp) cv kc|ij }l pvcql zdl z}c {zlp{ bg lbzdlv cvjlv3

;' Ilz P$g" fl h pvljbkhzl ca ghz|vhi g|eflv{' [|ppc{l }l pvcql zdl aciic}bgm ahkz{?

P$0" dcij{ P$8" dcij{ acv hgr b 0) baP$b" dcij{ zdlg P$b . 6" dcij{

Jcl{ zdb{ kcg{zbz|zl h qhibj pvcca zdhz P$g" dcij{ acv hii g G3 O|{zbar rc|v hg{}lv'

:' Ilz P$g" fl h pvljbkhzl ca zdl bgzlmlv{' [|ppc{l }l pvcql zdl aciic}bgm ahkz{? P$0" dcij{ acv hgr b 0) baP$b" dcij{ zdlg P$b . 8" dcij{ acv hgr b 0) baP$b" dcij{ zdlg P$b 8" dcij{

Jcl{ zdb{ kcg{zbz|zl h qhibj pvcca zdhz P$g" dcij{ acv hii g _3 O|{zbar rc|v hg{}lv'


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Zd|{) P$b" dcij{) h{ }hgzlj'

Kilhvir) dc}lqlv) }l khgz ehnl hg cjj hec|gz ca pc{zhml |{bgm cgir :%klgz hgj 1%klgz{zhep{( Zd|{) zdl {zhzlelgz P$g" dcij{ acv hii g : b{ klvzhbgir ahi{l' Kcg{lx|lgzir) zdlhfcql pvcca b{ bgkcvvlkz' ]dhz b{ }vcgm }bzd bz38:' Jlgl zdl {lx|lgkl ca bgzlmlv{ h0) h8) h6) h{ aciic}{?

hb 5

6) ba 0 b 6hb8 . hb6 . hb;) ba b 7 6

\{l kcepilzl bgj|kzbcg zc pvcql zdhz hg 9 6g) acv lqlvr bgzlmlv g 6'

8


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Kdhpzlv 6

KCVVLKZGL[[ CA BZLVHZBQLHGJ VLK\V[BQL PVCMVHE[

6'8 Pvcmvhe kcvvlkzgl{{

]dlg }l {hr zdhz h pvcmvhe b{ kcvvlkz) }l elhg zdhz bz pvcj|kl{ h kcvvlkz c|zp|z cg lqlvrhkklpzhfil bgp|z' Ca kc|v{l) }dhz lthkzir b{ h kcvvlkz c|zp|z hgj }dhz hvl jllelj h{hkklpzhfil bgp|z{ jlplgj{ cg zdl pvcfile zdhz zdl pvcmvhe b{ jl{bmglj zc {ciql l'm') babz b{ h pvcmvhe zc {cvz hvvhr{) cv h pvcmvhe zc {ciql {r{zle{ ca ibglhv lx|hzbcg{' Zd|{) }dlg}l zl{z zdhz c|v pvcmvhe jcl{ zdl vbmdz zdbgm fr v|ggbgm bz cg {cel {lilkzlj {lz ca bgp|z{ }lhvl gcz pvcj|kbgm kcgki|{bql lqbjlgkl zdhz zdl pvcmvhe b{ kcvvlkz' ]l hvl) hz fl{z) mhbgbgmkcgjlgkl zdhz zdl pvcmvhe b{ gcz bgkcvvlkz' Zc pvcql zdhz h pvcmvhe b{ kcvvlkz }l e|{zmbql h {c|gj ehzdlehzbkhi hvm|elgz }dbkd {dc}{ zdhz zdl vbmdz c|zp|z b{ pvcj|klj cg lqlvr

hkklpzhfil bgp|z) gcz o|{z zdc{l cg }dbkd }l kdc{l zc zl{z zdl pvcmvhe'Bzlvhzbql pvcmvhe{ $b'l') pvcmvhe{ }bzd iccp{" pvl{lgz h {plkbhi kdhiilgml bg zdb{ vl{plkzflkh|{l) bg mlglvhi) zdl g|eflv ca zbel{ zdhz h iccp b{ ltlk|zlj jlplgj{ cg zdl bgp|z' Zdl{hel b{ zv|l hfc|z vlk|v{bql pvcmvhe{' Kcep|zlv {kblgzb{z{ dhql jlqlicplj klvzhbg zlkdgbx|l{acv pvcqbgm zdl kcvvlkzgl{{ ca {|kd pvcmvhe{' Zdl{l zlkdgbx|l{ vlir dlhqbir cg bgj|kzbcg' Bgzdb{ kdhpzlv }l }bii lthebgl zdl{l zlkdgbx|l{'

6'6 [plkbkhzbcg zdvc|md pvlkcgjbzbcg{ hgj pc{zkcgjbzbcg{

Abv{z }l gllj zc jb{k|{{ dc} zc {plkbar }dhz hvl zdl hkklpzhfil bgp|z{ ca h pvcmvhe hgj }dhzhvl zdl kcvvlkz c|zp|z{ acv lhkd hkklpzhfil bgp|z' Cgl kcgqlgblgz hgj pcp|ihv }hr zc jc zdb{

b{ fr |{bgm pvlkcgjbzbcg{ hgj pc{zkcgjbzbcg{' H pvlkcgjbzbcg acv h pvcmvhe b{ hg h{{lvzbcgbgqciqbgm {cel ca zdl qhvbhfil{ ca zdl pvcmvhe> zdb{ h{{lvzbcg {zhzl{ }dhz e|{z fl zv|l flacvlzdl pvcmvhe {zhvz{ ltlk|zbcg bg phvzbk|ihv) bz khg jl{kvbfl }dhz hvl jllelj h{ hkklpzhfilbgp|z{ acv zdl pvcmvhe' H pc{zkcgjbzbcg acv h pvcmvhe b{ hg h{{lvzbcg bgqciqbgm {cel ca zdlqhvbhfil{ ca zdl pvcmvhe> zdb{ h{{lvzbcg {zhzl{ }dhz e|{z fl zv|l }dlg zdl pvcmvhe lgj{ bg phvzbk|ihv) bz khg jl{kvbfl }dhz b{ h kcvvlkz c|zp|z acv zdl mbqlg bgp|z'

Mbqlg h pvlkcgjbzbcg#pc{zkcgjbzbcg {plkbkhzbcg hgj h pvcmvhe) }l {hr zdhz zdl pvcmvhe b{

:=


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:4 KDHPZLV 6' KCVVLKZGL[[ CA BZLVHZBQL HGJ VLK\V[BQL PVCMVHE[

kcvvlkz }bzd vl{plkz zc zdl {plkbkhzbcg $cv zdl pvcmvhe ellz{ zdl {plkbkhzbcg") ba }dlglqlvzdl pvlkcgjbzbcg dcij{ flacvl zdl pvcmvhe {zhvz{ ltlk|zbcg) zdlg $h" zdl pvcmvhe zlvebghzl{hgj $f" }dlg bz jcl{) zdl pc{zkcgjbzbcg dcij{' Aciic}bgm hvl {cel lthepil{ ca pvlkcgjb%zbcg#pc{zkcgjbzbcg phbv{ acv {cel {bepil f|z |{la|i {plkbkhzbcg{' Bg zdl{l gczl{ }l h{{|el

zdhz zdl {zhvzbgm bgjlt ca hvvhr{ b{ 8) hgj zdhz ilgmzd$H" b{ zdl g|eflv ca lilelgz{ ca hvvhr H'

Lthepil 6'8 [|ppc{l }l hvl bgzlvl{zlj bg h pvcmvhe }dbkd) mbqlg hg hvvhr H hgj hglilelgz t) {lhvkdl{ H acv t hgj vlz|vg{ zdl bgjlt ca h pc{bzbcg ca H zdhz kcgzhbg{ t> ba gcpc{bzbcg caH kcgzhbg{ t) zdlg zdl pvcmvhe vlz|vg{ 0' [|kd h pvcmvhe khg fl {plkblj fr zdlaciic}bgm pvlkcgjbzbcg#pc{zkcgjbzbcg phbv'

Pvlkcgjbzbcg? H b{ hg hvvhr'

Pc{zkcgjbzbcg? Vlz|vg hg bgzlmlv b {|kd zdhz 8 b ilgmzd$H" hgj H^bU 5 t) ba {|kd hgbgzlmlv ltb{z{> czdlv}b{l vlz|vg 0'

Gczl zdhz zdb{ {plkbkhzbcg jcl{ gcz zlii |{ dc} zc {lhvkd H acv t' ]l khg ellz zdl{plkbkhzbcg }bzd h pvcmvhe zdhz {lhvkdl{ H avce zdl v{z pc{bzbcg zc zdl ih{z) cv avce zdlih{z pc{bzbcg zc zdl v{z) cv bg hgr czdlv cvjlv'

[zvbkzir {plhnbgm) zdl pc{zkcgjbzbcg bg zdl hfcql {plkbkhzbcg {dc|ij hi{c {zhzl zdhz zdlqhi|l{ ca H hgj t hvl gcz hizlvlj fr zdl pvcmvhe' Zc {ll }dr) kcg{bjlv zdl pvcmvhe zdhz {lz{H^8U ?5 t hgj vlz|vg{ 8' Zdb{ pvcmvhe jcl{) bgjllj) vlz|vg zdl bgjlt ca hg lilelgz ca H zdhzkcgzhbg{ t) f|z bz jcl{ {c fr kdhgmbgm H) gcz fr {lhvkdbgm bz( Flkh|{l bz flkcel{ zljbc|{ zcltpibkbzir {zhzl zdhz qhvbc|{ qhvbhfil{ hvl gcz kdhgmlj fr zdl pvcmvhe) }l hjcpz zdl kcgqlgzbcgzdhz) |gil{{ {zhzlj czdlv}b{l) hii qhvbhfil{ elgzbcglj bg zdl pvlkcgjbzbcg hgj pc{zkcgjbzbcghvl gcz hizlvlj fr zdl pvcmvhe' Lgj ca Lthepil 6'8

Lthepil 6'6 [cel pvcmvhe{ zdhz {lhvkd hg hvvhr acv hg lilelgz }cvn kcvvlkzir cgir ba zdl

hvvhr b{ {cvzlj'8 Zc {plkbar {|kd h {lhvkd pvcmvhe) zdl hjjbzbcghi h{{|epzbcg zdhz zdl hvvhrb{ {cvzlj e|{z fl bgki|jlj bg zdl pvlkcgjbzbcg' Zd|{) acv {|kd h pvcmvhe) zdl pvlkcgjbzbcgmbqlg hfcql }c|ij fl vlpihklj fr

Pvlkcgjbzbcg? H b{ h {cvzlj hvvhr'

Zdl pc{zkcgjbzbcg vlehbg{ h{ bg Lthepil 6'8'H pvcmvhe zdhz {hzb{l{ zdb{ {plkbkhzbcg khg ltdbfbz hvfbzvhvr fldhqbc|v ba zdl mbqlg hvvhr

b{ gcz {cvzlj? Bz ehr vlz|vg hg bgjlt zdhz kcgzhbg{ hg lilelgz czdlv zdhg t) bz ehr vlz|vgh qhi|l zdhz b{ gcz hg bgjlt ca zdl hvvhr) bz ehr glqlv vlz|vg h qhi|l) cv bz ehr kh|{l zdl

kcep|zlv zc kvh{d( Lgj ca Lthepil 6'6

8Hg hvvhr b{ {cvzlj ba bz{ lilelgz{ hpplhv bg gcgjlkvlh{bgm cvjlv' Ecvl pvlkb{lir) H b{ {cvzlj ba) acv lhkd z{|kd zdhz 8 z 9 ilgmzd$H") H^zU H^z . 8U) }dlvl b{ h zczhi cvjlv ca zdl jhzh zrpl zc }dbkd zdl lilelgz{ca H flicgm' $]dlg }l {plhn ca h {cvzlj hvvhr }l hvl) bepibkbzir cv ltpibkbzir) h{{|ebgm h zczhi cvjlv ca zdljhzh zrpl{ zc }dbkd zdl hvvhr lilelgz{ flicgm' Acv lthepil) ba zdl hvvhr lilelgz{ kcgzhbg bgzlmlv{) zdl zczhicvjlv kc|ij fl zdl cv vlihzbcg cg bgzlmlv{> ba zdl hvvhr lilelgz{ kcgzhbg {zvbgm{) zdl zczhi cvjlv kc|ij fliltbkcmvhpdbk cvjlvbgm'" Gczl zdhz) bg mlglvhi) h {cvzlj hvvhr ehr kcgzhbg j|pibkhzl{'


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6';' KCVVLKZGL[[ CA FBGHVR [LHVKD :2

Lthepil 6'; [|ppc{l }l hvl bgzlvl{zlj bg h pvcmvhe }dbkd {cvz{ h mbqlg hvvhr' [|kd h

pvcmvhe khg fl {plkblj fr zdl aciic}bgm pvlkcgjbzbcg#pc{zkcgjbzbcg phbv'

Pvlkcgjbzbcg? H b{ hg hvvhr'

Pc{zkcgjbzbcg? H kcgzhbg{ zdl {hel lilelgz{ h{ flacvl zdl bgqckhzbcg) f|z bg {cvzlj $gcg%jlkvlh{bgm" cvjlv'

Gczbkl zdhz zdb{ {plkbkhzbcg hiic}{ acv H zc fl hizlvlj fr zdl pvcmvhe hiflbz bg vl{zvbkzlj}hr{) ghelir fr vlhvvhgmbgm bz{ lilelgz{' Lgj ca Lthepil 6';

[plkbkhzbcg{ ca zdl nbgj bii|{zvhzlj fr zdl{l lthepil{ hvl qlvr bepcvzhgz bg pvhkzbkl'Zdl {bgmil ec{z bepcvzhgz lilelgz ca mccj jck|elgzhzbcg acv h pvcmvhe b{ zc kcgqlr o|{z}dhz zdl pvcmvhe jcl{ $pc{zkcgjbzbcg{" hgj |gjlv }dhz kcgjbzbcg{ bz b{ ltplkzlj zc jc bz$pvlkcgjbzbcg{"' Zd|{) h }lii%jck|elgzlj pvcmvhe e|{z bgki|jl) hz h ebgbe|e) h pvlkcgjb%zbcg#pc{zkcgjbzbcg{ phbv zdhz kcg{zbz|zl{ bz{ {zhzlelgz ca kcvvlkzgl{{' Pvcqbjbgm {|kd h {plkb%

khzbcg b{ kv|kbhi vlmhvjil{{ ca }dlzdlv cgl bgzlgj{ zc khvvr c|z h jlzhbilj pvcca ca kcvvlkzgl{{acv zdl pvcmvhe' Zdb{ b{ flkh|{l h pvcmvheelv }dc }b{dl{ zc |{l hg ltb{zbgm pvcmvhe {dc|ijfl hfil zc jc {c fr vlhjbgm o|{z zdb{ {plkbkhzbcg) hgj }bzdc|z dhqbgm zc iccn hz zdl kcjl'

Zdlvl hvl ehgr acvehi gczhzbcg{ zdhz dhql fllg jlqlicplj acv ltpvl{{bgm pvlkcgjbzbcg{hgj pc{zkcgjbzbcg{) lhkd }bzd bz{ hjqhgzhml{ hgj jb{hjqhgzhml{' [cel ca zdl{l gczhzbcg{ vlirdlhqbir cg pvljbkhzl icmbk) h {|folkz zdhz }l }bii lgkc|gzlv bg Kdhpzlv 1' Bg zdl{l gczl{ }l}bii gcz fl kcgklvglj }bzd acvehi gczhzbcg{ |{lj zc ltpvl{{ pvlkcgjbzbcg{ hgj pc{zkcgjbzbcg{>}l }bii ltpvl{{ zdle bgacvehiir zdc|md dcpla|iir kilhvir hgj pvlkb{lir bg Lgmib{d'

6'; Kcvvlkzgl{{ ca fbghvr {lhvkd

Fbghvr {lhvkd b{ hg himcvbzde }dbkd) mbqlg h {cvzlj hvvhr H hgj hg lilelgz t jlzlvebgl{}dlzdlv t hpplhv{ bg H hgj ba {c bz hi{c jlzlvebgl{ hg bgjlt ca H zdhz kcgzhbg{ t' Zd|{) zdl{plkbkhzbcg ca zdb{ himcvbzde b{ zdhz mbqlg bg Lthepil 6'6' Bgacvehiir) fbghvr {lhvkd }cvn{fr kcephvbgm zdl zhvmlz lilelgz t zc zdl ebjjil lilelgz ca H' Ba zdl ebjjil lilelgz b{mvlhzlv zdhg cv lx|hi zc t) zdlg zdl {lhvkd b{ kcgglj zc zdl v{z dhia ca H> czdlv}b{l) zdl{lhvkd b{ kcgglj zc zdl {lkcgj dhia' Zdb{ pvckl{{ b{ vlplhzlj |gzbi zdl {lhvkd b{ kcggljzc h {|fhvvhr ca {bl 8) bg }dbkd kh{l zdl bgacvehzbcg {c|mdz fr zdl himcvbzde b{ zvbqbhi zcjlzlvebgl' Zdb{ himcvbzde khg fl ltpvl{{lj lbzdlv bzlvhzbqlir) bg }dbkd kh{l lhkd dhiqbgm cazdl hvvhr kcvvl{pcgj{ zc hg bzlvhzbcg ca h iccp) cv vlk|v{bqlir) bg }dbkd kh{l lhkd dhiqbgmkcvvl{pcgj{ zc h vlk|v{bql khii'

Zdl bzlvhzbql qlv{bcg ca fbghvr {lhvkd b{ {dc}g bg Abm|vl 6'8) }dbkd hi{c kcgzhbg{ zdlpvlkcgjbzbcg{ hgj pc{zkcgjbzbcg{ vlihzbql zc }dbkd }l }hgz zc pvcql zdl kcvvlkzgl{{ ca zdlpvcmvhe' $Zdl a|gkzbcg jbq }h{ jlglj cg phml 64'" Zdl pvcmvhe |{l{ z}c qhvbhfil{) a hgj zdhz bgjbkhzl) vl{plkzbqlir) zdl v{z hgj ih{z bgjlt ca zdl vhgml zc }dbkd zdl {lhvkd dh{fllg kcgglj {c ahv' Ba zdl vhgml b{ gcgzvbqbhi $b'l') dh{ ecvl zdhg cgl lilelgz") zdl ebjjilbgjlt ca zdl vhgml b{ kcep|zlj h{ qhvbhfil e) hgj zdl vhgml b{ kcgglj zc zdl hppvcpvbhzldhia'


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czdlv}b{l bz vlz|vg{ 0'

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8 a ilgmzd$H") hgj ba t b{ bg H zdlg t b{ bg H^a''U' $6'8"


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6';' KCVVLKZGL[[ CA FBGHVR [LHVKD


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6';' KCVVLKZGL[[ CA FBGHVR [LHVKD


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6':' ZDL KCVVLKZGL[[ CA H E\IZBPIBKHZBCG PVCMVHE zc bgzlmlv%jbqbjl h g|eflv fr 80) }l jvcp zdl vbmdzec{z jbmbz'


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b'l') ba zdl iccp b{ ltlk|zlj hz ilh{z o . 8 zbel{) zdlg o.8 5 eg to.8ro.8'

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bz zdlg {lz{ t zc 81 hgj jlkvlelgz{ r cgkl' Zdb{ b{ vlplhzlj |gzbi fczd t


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6'


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10 KDHPZLV 6' KCVVLKZGL[[ CA BZLVHZBQL HGJ VLK\V[BQL PVCMVHE[

]dlvl jbj zdl ltpvl{{bcg 8=r . t kcel avce3 Zdl bgacvehi jl{kvbpzbcg ca zdl iccp mbqlglhviblv $jlkvlelgz t |gzbi bz flkcel{ 0) zdlg {lz bz zc 81) jlkvlelgz r cgkl hgj vlplhz |gzbifczd t hgj r hvl 0" {|mml{z{ zdl aciic}bgm bgzlvpvlzhzbcg acv zdb{ iccp' Zdbgn ca t hgj rh{ zdl jbmbz{ ca h z}c%jbmbz g|eflv bg fh{l 8=) }dlvl t b{ zdl ic}%cvjlv jbmbz hgj r b{ zdl

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6'1' KCEELGZ[ CG PVCQBGM ZDL KCVVLKZGL[[ CA BZLVHZBQL PVCMVHE[18

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iccp bgqhvbhgz' Zdb{ pvckl{{ b{ vlplhzlj |gzbi }l pvcj|kl h pvcpc{lj iccp bgqhvbhgz zdhzb{ {|kblgz zc pvcql phvzbhi kcvvlkzgl{{'

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6'=' PVCCA CA KCVVLKZGL[[ CA VLK\V[BQL PVCMVHE[ 1;

EhbgFbg[lhvkd$H) t" Pvlkcgjbzbcg? H b{ h {cvzlj hvvhr ca ilgmzd hz ilh{z 8' Pc{zkcgjbzbcg? Vlz|vg z {|kd zdhz 8 z ilgmzd$H" hgj H^zU 5 t) ba {|kd h z ltb{z{> czdlv}b{l vlz|vg 0'

vlz|vg VlkFbg[lhvkd$H) 8) ilgmzd$H") t"

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Abm|vl 6':? Vlk|v{bql fbghvr {lhvkd

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1: KDHPZLV 6' KCVVLKZGL[[ CA BZLVHZBQL HGJ VLK\V[BQL PVCMVHE[

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hadzilacos vassos - intro to theory of computation

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