Gi,i tr! I', gQi la gi<i tri kfch hm,lt vi n6 eho ph~p d.c 16i Ian truycn qua phAn tu tai d,-lu nl. Tren hLnh 8.7, dua fa vi eh.1 ve ph~in tir NA: ID thoa man m~nh de Hen. Ph,-In IU: NA; JD nay se c6 tAt d cae d,lu vao nh(11l gia Irj 'I' ho,k l[l( d nhiIng duu vao n1<1.n cam nh(m gi,i Irj '0' Y~I nhO"l1g dau elm 1'.li duqc d~lt gia trj 'I'. I\'CL! t<-l ,ip dl,lng phein :3 ella m~nh de tren I,)p h,li nhicu Ifin, chung ta sc nh(ul dtfQe he qu,-i saL! \'6 UIC dLf('-mg dJn m,ln dm v6i 16i: H~qml Gii.l thic"t duang tin hi¢uj man dm \'61 16i hb.ng so gi,i lrj I' S-(I-I'f(tLwng Lrng vai vcctO' gi,i trj kiem nghi¢m t phat hi~n 16i ) va p Iii. gia tfj ngh!ch (Lto eLIa duang man dun loi giG'afva,;. Klli d6 gia trj eua) lrong veeta t Iii. l' GJ p. Ne"u co m()t s6 (hl'ong tin hi~u nhi;lY dm giila f \,~l J Ihl IAI d C,-lc duong do (h~lI cllilg nh,)n gii.l tr! nghjeh (h-to p. c. Kha nang phat hj~n lui Do de di~m quan sal chi gi6i lwn (,.ti d.e (tiu vao \'a driu ra ( co nghTa I~I vi~e kic'm tra chi duqe thlfc hi¢11 Iheo gia Ir! ella ham fa ) nen ec1 the x,iy ra Iruling IHJp co llh[C!1g 16i kh6ng phat hi~n duqe ho;)c ell nh[Ing Illi khtlllg ph,tn bi~t duqc. M9t J6ilduqc gQi IA e6 th~ phat hi~n duqe nc"u ton t'-,Ii \'eeto' gi:i trj him nghi¢m t ph,-it hi¢n dUQ'c f Trong lruo-ng hqp IlgUQ'C I<;l-i, 16i I duqc COl Iii khlmg tilt phal hi~n dU<;1e. Nhung 16i f kll6ng the phat hi¢n dLf<;1e la nhGng 16i lam eho gi,i tr! hi"tm fa khong thay dbi so sanll y6'i tmong hQ'P trong nwch khong co loi. Nhu Y(ly ta co L"/ t ) = 2( t ), hay e6 the n6i c<ich khac I) t ) = O. Khi d6 kh6ng the co \'ccto' gi,i tr~ kicll1nghi~m !liIO co the kich hm,lt qUii trlnh lruycn (6ifv~\ (!ling thO'i lao fa du(mg dan man cam voi loi r den d,l.u ra chfnh ella m'.leh. Nhu'lll,! loi kh6ng the phiit hi¢n duqe gQi la nhilng lui du fhim v,1 nhO"ng mi,leh tl; h9'P ehLJi.l nhung 16i hang so dLf thua duve duqe gQi la lll::,Ich du fhl'm. 255 A~~~ , j I-L __ J , jLJ- ,I J, DO I r_ 1 C "1""1 I )-' Ilillh 1'i.1'i. \llIlil lin,! Inrim12 ho'p kh()l\g ph.d hlL'1l dU'ljl' Ill! iii! tron);! Illalll. Vi tll.1. \'6i m<.lch tfen hlnh ~~. lili himg s(i Iren dlftmg lill hlC"u (1.1'- (/-} (/11 1;1 liil ~hhng IhC: ph,il bien dlfP'C. Nhung I(\i ~h()IlS ph'll hi~n duoe n{ll Irell u\ IhC: hr') qua \,'1 Chlillg ~h(lllg !:till Iha\' (kil l'llLk' Jl,~ll1g IClt!lC etta mach nlumg s~r c6 m,H clla de I()i ll~ty C() Ih~ ph:i v c:ia Ihk,'t n~ dicu ~il'll Imllg 111'.ICh chi c6 m()1 161 \'~l e6 Ihe: dtlll tkn nllLfng ~l'l lIlt,\ \ai. I\e'u d~r<l Hen chIC·'n lu(/c ~iC:1ll tr;] (1ll1tmg XUyCll. e6 Ih~ gi,i thi0'l r:lIlg Chl!llg la : ': ph"11 !lIen c1U"ljc Ii)i IrLf(k ~h] j(li thlf hai XU:lI hicn. Nhung dicli Il~l\' c6 the kh()Il~' tllLrc Khl eh~'lng la 1,.tO fa de \'l'CICi gi,i tq Ihlr nghi¢m clIO m()t mach. 1ll111' dlcll chfnh EI Un dW.K nH)( \(Ip hqp (by elll c,ie \'l'eto' gi,\ II"! klCIl1 ngllll'lll dC: plt;;1 Wnh 1'1,1), ;\Ill! hll('mg ella 10] (/1/ khl)ll)!. plliit 11I':1l dlroC troll)!. llwdl I('ii, ICC ph~il hi211 101 tlll'r hai /ill!, hien kll. 'L:lp hl.l"p Il;l) \0 clio ph0p ph;il hien llHll I(l] c6thC: ph;il hien dunc Tuy nhieJl. 1;1[1 IHl'P n;l) cling kh6I1g dl'l dl: ph.!l hien lll()i ](11 U) I Ill: phdl d troe llL'U Illach 11111 \;.Ii nhll"llg k)i c111i'a dlf(.l'C phcil btL'Il. Vi duo (lllllg 1ll'.lch tfell hlllh S.lJa. I(\i htlllg ',(j (ll'll dUlfllg lin hicu II ,\-{,.{) I~\m cho gt:i Ir! dU'(\lIg 1:1 '0' lij() et) thc dune ph:tt hi~'Jl ne'li su dung \'L'C\(f giii II"! ki2m nglllelll ( = "J 1 0 I ". L6i n;IY Iro' Ih;\Jlh kh(lIlg rlr.it hi¢n du\l'C Ilc'u trong m' \Ch co 16i hilllg so all .1'-(/-]( hlnh 8,9b). Trui)ng Ill.JP I(ln li.li m(l\ lui kh(llIg ph,lt hien dm/e ngtlll ch~n \'i¢e 11m de 1(\1 kh,k lrong 1I1\lch kh(mg: chi gi6'i han trong vi~c tlm nhO"ng It)i cling 10'.li (nhu truO"llg h(.Jp cae 16i htll1g s6 ,'ll1h hUO"llg 16i cac 16i hang s6) II1It con c6 Ih0 dung d6i \"6i nhCfllg loi kh,\c loai, VI du nhu: llll)t 16i h 1c cal. khong pkl\ hi9n dW1"C co Ih~ I~\in cho vi2c ph,!1 hi~lI loi c6 dPlh khac khong the th\.fC hi¢n Chf()"C. Ta hay XCl VI ell.L nwch In~ll hlnh 8.10. M •. \Ch lren hlnh 8.10 111m: lu¢n hilllll6gic: I\' == xv + x: LUI b~c C<lU OR giCra dU0ng tin hicu Y V;I x 1;1 khong phat hi~n dWK vi: Trcn hlnh l).IOa, ta thAy \'i:clO gia Ir! kicm nghicm t ::; "Ill" cho phep ph,-!! hi~1l 16i hill1g so s-(/-() trcn dlf0ng tin hi¢u q qlO. Khi trong 111'.lch xuilt hi~n l6i h{lc d.lI OR noi Ircn Ibl vcetci gi,\ lri kl0'm nghi2m nay kh6ng the ph,1! hlcn duqc loi qlO (hloh l(lOb). Ta nh(\l1 th:iy I(IJ) hqp c,ic \'L'CW \.'i,\ tri kiC:m nohiclll C'. eo . T ~ {III. Olll, 001. 101 J I:, Up h(.1P dflY dl) de ph • .I\ hi¢n 16i king so don va wcto" t ::::: "111" b \'cctci gLa Ir! kicm nghi~'m lilly nh:it pil,\t hi¢n It)L (I/O. ;.JIllr - - IHnh KIO, ·Irulmg llqp loi htlc du OR khong ph;\t lllcn (tUl1C ,\\\11 11lllJng t(ll \'icc ph,i[ lW,'~ll 101 hall"", \,j (Iii!. \·,ly qp lll~p T tnj Ih~nh khtlng d:iy du khi Irong m~lCh xu:it hi¢n lbi klc du kh6ng. pilat hi¢n dune n6i tr0n. t-:hCt'l1g ll1<'lCh to hQ'p du' thlra co th~ dUQ'c dan gi,\n hoa btmg ci.lch IO~.li h6 flllh;!1 llll)t ph:in tV 16g.ic hO~le l1ll)t d:iu van eua plu111 tu, Vi dl}. £oia Ihie'l r<tng 16i /'s-o-] xuut hi¢n t~li d:iu VllO i eGa ph[lll IU AND lil kh6ng th~ phat hi~n duqe. Do chllc nflllg ella m'.leh kh6ng thay doi khi xu[it hi~n h"Ji I nen ta co the cl~11 gi~i If! 'I' t\ll.J"CHlg tr~rc 1i Li dflu \'ltO i nlly. Do ph;in tV AND voi /I d,tu 257 \'ilo trong d() co m()1 d,l.u \'~IO i nh~n gia trj '1' sc tuong c1uong \'6i pilfln tu AND v6i (II - 1) dilu V~IO, Trang eto rh::in tlr AND v6i (/I - \) dilu vi\() nhfm du\1'C IV ph[;n tv: II d<i.u \'UO ban d[iu bAng deh Im.li b6 d~iu \':10 i do. Tuong tLY nhu \"(Iy, nC:u phi"in tu AND co loi s-((-() t'.li d::iu \'il.O la kh(mg the tim duqe thl phiit1 tu AND do co the \O'.li b6 \'a tbay the bttng tin hi¢u '0'. '~-'-;,1DT- K ·D m y '1>'~ - ,! ~ 1-' I'\eu hai loi I \'01 g khi xuat hi~n t!"ong 1l1< lch [~\lll cho de h~lln ra ell;'l lll'.ICh Z/ x ) \';l Z,( x ) tilo,i mo1n he thLre Z/ x ) =: ZJ x ) Vx. khi do nhfrng It)i n~ly dUQ'c g{)L I~I tuong dunng vc m,1t i - "i~_' r ~' fW '- c > "" ,J w d ~I ~)- L./ L- Hinh ILl 1. Vi dll \'6 ItJllhr thi:ra vii loi wong lhrollp._ c1ule wing. v ccto gill lr! clciu vuo t lam hai loi f va g ph~lIl bi~t dw)'c neu Z,( t }:;<oL,( t ) \'i\ hai loi f \'U g .,(3 c1uqc gqi 101 phan bi¢t duqc, Chung ta khCJI1g tht' 11m du~)'C wetc1 gia Iri ki6m nghi¢m t cho phcp phun bi¢t hai 16i luong uuong \'e m~lt Chl:i'C n"Ill". ()uan he lUOn!! duoll" \'e 111:11 ehltc n[lIl" "IUa dc l<\i cho [)hcn to . L' e. to '" I' phCl1l 110'.lch t,)p hop cae hli thanh dc lOp lUang dU(J"llg, DJ phAn tieh Ir'll. chling ta chi dll khao sat !llt)1 16i d,!i di¢n cho tung IClp Wong duong. Ta hay xci VI d'-:l Lllach tll h(fP tr~n hlnh X.II. IUm ra cLla H1<,lch c{) c\,.mg: - - :::::::: Z( x, y, H' )::::: ~\ + Y + .r y \1' !\'cu trong Ill~.\(;h xu:;t hi0n IClI hflt1g so j/O ta sc co : Zf,'lJ( X,)', Ii' ) ::::: Z( x, y, Ii' ) V,-~y Illij/O la loi du' thira. Neu trong mi Ieh xuflt hi¢n I<')i hang s6 dll ho~\c 171 thl: Z"fI( .r, y, \-\' ) ::::: Zfi/( x, )', w) = x + y V,:IY c,ic ltli hf1ng so dll vil.f!J la nilung loi lUang duong, Tuong tLy nhu \")y. cae loi h~\ng sojlO V~l If{) cCing 101 nhCi"ng loi luang duong, Ciic illi dLT thLIa va wong duong 101 h¢ qua cLla vi¢c xct llwch iiI m()t h()p den va ehi quail Sal hanh vi clla mi lch qua cac driu vao va (1[\u ra cu,\ Il1Hch. Neu \01 C() lh~ quan sat gla tf! tin hi¢u t,-li nhung duo-ng truy~n bell trong 1l1i \Ch thl nhung loi nay sc phat hL¢1l duqc. Nc'u chung ta dua ra phuong pllap 258 xJe dinh dll\K kh6ng nhCrng Sl,f I(m 1<,11 ella Illl m:1 ebn Y;I chi ra dUl,l'C \! lri h\l. 1111 phuong pll<ip d6 gqi \:1 pllll'Ong phJp cilldn ,hill I,ll. D6i y6i hai l()i hAL kS (Y:I g. clll'lng ta x,\c dinll !J;lln kho,lng c,ich giCr<l ll,ti loi do nil It' SHU: F,/ x ) = I) x 1 6l I) x 1 = 1,< x 1 (j) 1/ x 1 Nc'u ycell1 gi,i Iri lilu nghi0111 t I:un eho FrO< t) = L la n6i dlllg \'CcLo gi,i Lf! tllLr nghi~1l1 t pll:l1l bi¢L hdi I(\i f g Y~\ dlt'CiC k)' hl¢U 1:1 t'~. eil,i tlll.?L rimg P 1:1 hlp hop c,ic It\l e6 the' (.J) \';1 m',Kh du(.l'c thid k0 1 lH'lllg chiI'd \(\i. Nell c\lllllg 101 '(,Ie dinh I,)P h0P L,YI C't nhCrng \'I 'c1o' gl,i If! kiC:Ill nghi¢m phtm hic\ hai leJ! b,lI k5' T = 1 rR) dcii \'6i nH1l ph:lll Ill' lhul)l' L:tp 111.111 P till 1,)P h(,)p T = I rl' ) 11\1 Ih,lnh I,IP hq'p de YCl'lo gi,i Iri tillr nghi0111 clIO phcp II1l,fe hl¢n \'i~c ehu,\ll doun l/ii Y:I lhr(l'c gqi lit 1<)P hl}'P C,-Ie \'celO ChU;)11 d(),in \(\i. N61 chung. khi :\lIAI hien c<.Ie Illi (lfong tinting. cllling la Can ,",Ie dinh I:IP 11(.1'11 dc YcelO" chu:in (\o,in d6i nii nhC-fIIp. It'll dal di~'n cilo de kip Illi tuong dll\1Jlg n: 111,)1 c\llk n:mg. Vi dL,l. clUing ta :\Cl m'.ICh bi0u di~n (r01l hlnh X.12: Nc'll x,le dinh de loi htUlg so S-i/-() • .1'-(/-/ tren e ic dUllllg Il'llycn till hl~'ll ella Il1Hch. la C{) e,ie ph:1ll nhol11 Illi nllLT sau: I" =1,., =1" =1" = I" = 1" = L,,, =1"., = I: - /','~I:: y + 11': L ul = X.Y w: L",,) = 0; L~,~,=x+ v+ \\': 259 x , Y b w , k 9 h d IIlnh S.ll. Vi flu I11lllh hoa e110 viec ellUin do,in loi bang cae \TCIO gJa In lhLll1ghlt':m. di¢ll dU\K at1u ra trong bang sau: r=;::::!i[iU van ,x y w alI a/O b/l 0 () ! I 0 0 I 0 I 0 0 0 0 rE - I I I 0 0 - I 0 0 0 () - i I I I 0 I 0 - z Lui d/l 0 I 0 0 0 trong do du loi gj() iiI I()i thlf<l \'1 Z"ilJ( x ) =: Z( x ). Nluf "rlY ChUIl" la thil)' rtlll" b t- chung la co bilY U)] d'.li dicll. eic \'ec1o' gi<i Ir! J iem nghi~m d~ chu[ln c10an cae loi (1.,11 :=1 e/O k/O 110 I I I 0 0 -,- I 0 0 0 0 I I I I I .,_ J Tic hang n~IY ta thfiy, d6i v6i moi C{lp U)il g 11.1 deu co the tim duqc n:cW gUt Ir! o,-lu vao t phan hi~t chung ( co nghi<-L til. F,c'( I ) = I ). Do d6, L)p iWp c,ic "ccto gia lrj kiC:m nghiem lrong h,ing El tflr hqp cliu[ln dO(Ul C(lC teli ht\llg s() lrC:11 cic duang l!ll hi~lI lrong l11<.\ch to hc:p. B,ing chua de gia If! eLla h;lin kho;ing kho<l!lg deh Illi Fl x ) doi \'O'i cae \'cele5 gia tfj thu: nghi¢m t viI 16j.l gQI ta bang chuan doan l6i. 2. Phat hien hli trong l1l<,lch tuan t~( Kiclll Ira cUc mi leh luan II! phuc ti,lP han so vO'i trui1ng IH:fp l1l' lch 1(; IH.1p. Dc co Ihe rh<.it hi¢n dU<;ic \oi, chung la can phai Slr dl,mg chuM de vecll1 gia Irj kicll1 nghi~m va dap ung eua mi.leh tu.l.n tl! se I~l h~l1n d6i \,t~i de In.\Ilg th<.ii ban dilu ella mach. Chung ta se elva ra tnQl so' minh hO<,l qu.! trinh phi!t hi~n I{lI eho mach tuan tt.e (Ji<'\ thiet T \a chuoi veeta gia trj thtr nghi~tn va R( (j, T) hI dar u'ng ella 1l1i.leh tu,-ln til N doi vai ehuoi T b{lt dil.u tlr tn.tng thai (j. Gj,l thie! rang khi trong nweh N XUii't hi¢n lui j: nweh N tny thinh ll1i.lch N{ va R/ (j{ ,1' ) ];\ (kip ung ella m,)ch ehl"ra loi N{ doi vai ehuoi l' btlt dilu Itt tn.tng thai (II" Chl"mg ta elva ra djnh nghla sau: 260 Chuoi T dc yeclci gili Iri kiem nghi~m clulC clu1n phat hi~n loi r twng: m'.lch luun I~( ne'u \'~I chi ne'u de d,i[) ling duu ra R( (I, T ) viI R/ tf, ' T ) kiJ,ic nhau \'6i moi C~I[) trang Ih,ij ban cUu q va (jr Tren hlnh H.13 aua ra m'.lch lu[in II! \'oi Mng chuy0n trang Ih,ii, day gi'l Irj tin hi¢u dUll ra \;\ d:lr CfIlg cLla ll1<,lch doi \'O'i day lin hi¢u ctl.u \,~I() T:::; I()I I I lrong In1cmg h0P nwch kh6ng co loi. Chung 1<1 xc! m'.lch trong nhling Inrbng hqp m'.lch chua loi hAng so f .1'-(1- / trcn dl1cmg (/ (1/ J , IrUlJ-ng hqr \,~l loi htmg s6 g S-(l-() trcll ducftlg b NO. Ta nhtUl th,!,), tSt c:t uic chu6i d,ip u'ng clla Ill<,lch khi chua loi g deu kh,\.c vai d,e d<.ip Cl"ng ella 111;.ICh khong chu'<\ l6i d6i v6"i cung mt?t t,ie d¢lI1g, nhl1 v~ly chu6i T noi tr2:n duk cklll ph:ll Iw:n dUq"c loi g. M;:ll khac, I1Wi dap lrng ella ml.LCh khong chCra It'li doi \'t)"j ChUlli T xel lil In.mg Ih;li khai I,.W B deu Irung vai dap u'ng ella m'.leh ehCra loi f xcI t<;li cung tn.lI1g thili but dfiu fl, nhu \'~)' chuoi T khong Ch[IC ch;'m ph<it y, f-' x z - y, y, y, y, D Q x y, y, c x a y, D Q x y, y, b C y, CL!< Hlnh 8.1.'. l\linh hoa Irucl"Ilg hop phM hi¢n 16i eho mach w{llI1l.r, 261 . nhling Inrbng hqp m'.lch chua loi hAng so f .1&apos ;-( 1- / trcn dl1cmg (/ (1/ J , IrUlJ-ng hqr ,~l loi htmg s6 g S-(l-() trcll ducftlg b NO. Ta nhtUl th,!,), tSt c:t. s-( (-( ) t'.li d::iu 'il.O la kh(mg the tim duqe thl phiit1 tu AND do co the O'.li b6 'a tbay the bttng tin hi¢u '0'. ' ~-& apos ;-; ,1DT- . n~ly dUQ'c g{)L I~I tuong dunng vc m,1t i - "i~_' r ~' fW &apos ;- c > "" ,J w d ~I ~ )- L./ L- Hinh ILl 1. Vi dll '6 ItJllhr thi:ra vii