Li ni uTrong cc nm qua, nhiu ti liu ca ngnh cng ngh thng tin c gii thiunhiu cho cccn bnghin cu, ng dng v sinh vin bc i hc. Tuy nhin cc gio trnh ca ngnh hc ny cha p ng dc nhu cu ca sinh vin cc trng i hc, c bit i vi sinh vin khu vc min Trung. V vy,chngtibinsongiotrnhTr tunhnto,mtmncs chuyn ngnh trong chng trnh o toCnhn Tin hc, ngoi mcch xy dng nhiu gio trnh trn mt khungchng trnh o to, m cn gipcho sinh vin c ti liu hctpph hp vi hon cnhthc tca ihc Hu.Trong cun sch ny, sinh vin clm quen vimts kinthcc bn nht v cc phng php tm kim li gii v cc phng php x l tri thc.Ngoi ra, cun schcng giithiumt s chng trnh ci t,nhmgip sinh vin c thhiumtcchtngtnccgii thut,ngthitintng rngccgiithutny c thp dungthct v ci t c trn my tnhmt cch d dng.Ccni dungtrnhbytrongcunschtngcgingchosinhvinngnh Cng ngh Thng tin ti i hc Hu trong nhng nm va qua.Cun sch ra i di s gip v mt vt cht cng nh tinh thn ca i hc Hu, Trng i hc Khoa hc v c bit l Ban ch nhim Khoa Cng ngh Thng tin v cc ng nghip thuc B mn Khoa hc My tnh. Chng ti xin gi ti h lng bit n. Xin chn thnh cm n cc bn b c c vgup cho cun sch sm c hon thnh.Mc d ht sc c gng, tuy nhin cun sch cng khng trnh khi nhng thiust. Chng ti rt mong c s gp ca cc c gi,c bit ivi cc ng nghip v sinh vin cun sch ngy cng hon thin.Hu, thng 7 nm 2004Tc giTi liu tham kho1. Bch Hng Khang, Hong KimTr tunhn to: Ccphng php v ng dng. Nh xut bnKhoahc v K thut, 1989.2. inh Mnh TngGio trnh Tr tu nhn to, i hc Quc gia H ni.3. Nguyn Thanh ThuTr tunhn to: Ccphng php gii quyt vn v k thutx l tri thc. Nh xut bn Gio dc, 1996.4. N. NilsonArtificial Intelligence. Ed. McGrawhill, 19715. Patrick Henry WinstonArtificial Intelligence. Ed. Addison Wesley, 1992..Mc lcChng 0. M u 21. Tng quan v Khoa hc Tr ru nhn to 22. Lch s pht trin ca Tr tu nhn to 53. Mt s vn Tr tu nhn to quan tm 84. Cc khi nim c bn 10Chng 1. Biu din bi ton trong khng gian trng thi 121. t vn 122. M t trng thi 123. Ton t chuyn trng thi 144. Khng gian trng thi ca bi ton 175. Biu din khng gian trng thi di dng th 186. Bi tp 21Chng 2.Cc phng php tm kim li gii trong khng gian trng thi231. Phng php tm kim theo chiu rng 232. Phng php tm kim theo chiu su 303. Phng php tm kim su dn 344. Phng php tm kim tt nht u tin 365. Tm kim ng i c gi thnh cc tiu - Thut ton AT 396. Tm kim cc tiu s dng hm nh gi - Thut ton A* 437. Phng php tm kim leo i 468. Phng php sinh v th 499. Phng php tho mn rng buc 5110. Ci t mt s gii thut. 5311. Bi tp 72Chng 3Phn r bi ton Tm kim li gii trn th V/Hoc 901. t vn 902. th V/Hoc 923. Cc phng php tm kim li gii trn th V/Hoc 944. Cy tm kim v cc u th 104Chng 4.Biu din bi ton bng logic v cc phng php chng minh 1071. Biu din vn h logic hnh thc 1082. Mt s gii thut chng minh 1303. V d v bi tp 138Chng 5. Tri thc v cc phng php suy din 1481. Tri thc v d liu 1482. Cc dng m t tri thc 1493. Suy din trn lut sn xut 152Ti liu tham kho 163I HC HUTRNG I HC KHOA HCGio trnhTR TU NHN TOHu, 20042Chng 0 M U1. Tng quan v khoa hc Tr tu nhn to.Trong Cng Ngh ThngTin, Tr TuNhnTo(ArtificialIntelligence) lmtngnh mi,nhng pht trinrtmnh mv em linhiu ktqu toln. Con ngithng tchomnh l sinh vt thngminh v khnng tr tu ng vai tr quan trong trong cucsng.Trong vn hccng tngcnhngcu chuyn cao v tr thng minh ca con ngi. Tr TuNhnTo chmi hnh thnh t nm1956. Tuy nhin, vic nghincu tr tu c t lu.Trn 2000 nm trc,ccnh trithc tm hiu v cch thcnhn nhn,hctp, nhv suy l. Vic raica mytnhint vonhngnm50cathk20sinhrakhuynhhngacclnhvc nghin cu tr tuv cc vn l thuyt v thc nghim trn my.1.1. i tng v mc tiu nghin cu ca tr tu nhn to.Tr tunhntonghincuvcchhnhxthngminh(intelligent behaviour) vimctiu l xy dngl thuyty vthng minh c th gii thch c hot ng thng minh ca sinh vt v p dng c cc hiu bit vo cc my mc ni chung, nhm phc v cho con ngi.- V mt k thut: To ra cc my thng minh gii quyt vn thc t dng cc k thut AI.- Khoa hc: Pht trin cc khi nim v thut ng hiu c cc hnhx thng minh ca sinh vt.1.2. Vai tr ca Tr Tu Nhn To. Tr tu nhn to bao qut rt nhiulnhvcnghin cuhp.N nghin cu tcclnhvctngqutnhmy nhnbit,suylunlogic, nccbi tonnh chi c,chng minh nhl.Thng th cc nh khoa hccc lnhvc 3khc tm n vi tr tu nhn to cc k thut h thng ho v t ng ho cc x l tri thc cng nh cc phng php thuc lnh vc mang tnh ngi.Tr tu nhn to nghin cu k thut lm cho my tnh c th suy nghmt cchthngminhvmphngqutrnhsuy nghcaconngikhiaranhng quyt nh, li gii. Trn c s , thit k cc chng trnh cho my tnh gii quyt bi ton.Sraiv pht trin ca Trtu nhnto tora mt bc nhyvt v chttrongk thutv k ngh x lthng tin. Trtunhn to chnhl c s ca cng ngh x l thng tin mi, c lp vi cng ngh x l thng tin truyn thng da trn vn bn giy t. iu ny c th hin qua cc mt sau:- Nhnhngcngchnhthcho(ccmhinhlogicngnng,logic m,...),cctrithc th tc v tri thcm tc th biudin ctrong my. Do vy qu trnh gii bi ton c tin hnh hu hiu hn.- Mhnhlogicngnngmrngkhnngngdngcamytnhtrong lnhvci hitrithcchuyn gia trnh cao,rt khnh: yhc, sinh hc, a l, t ng ha. - Mts phnmmtrtunhntothhintnhthchnghiv tnh mm do i vi cc lp bi ton thuc nhiu lnh vc khc nhau. - Khi my tnh c trang bcc phn mm tr tunhn toghp mngs cho php gii quyt nhng bi ton c ln v phn tn.1.3. Cc k thut Tr tu nhn to. C nhiukthutnghin cu,phttrinngnh khoa hcTrtunhnto. Tuy vy, cc k thut Tr tu nhn to thng kh phc tp khi ci t c th, l do l cc k thut ny thin v x l cc k hiu tng trng v i hi phi s dng nhng tri thc chuyn mn thuc nhiu lnh vc khc nhau. Do vy, cck thut Tr tunhn tohng ti khaithc nhng tri thc v lnh vc ang quan tm c m ho trong my sao cho tc mc tng qut; d hiu, d din t thng qua ngn ng chuyn mn gn gi vi ngn ng 4tnhin; dsai,hiuchnh,dsdng,khaithcnhmthuhpcckh nng cn xt i ti li gii cui cng.Cc k thut Tr tu nhn to c bn bao gm :- L thuyt gii bi ton v suy din thng minh: L thuyt gii bi toncho php vitccchng trnh giicu,chi cc tr chi thng quacc suy lun mang tnh ngi; cc h thng chng minh nh l. Ngoi racc h thng hi p thng minh cn cho php lu tr v x l khi lng ln cc thng tin.- L thuyttm kimmayri:L thuytny bao gmcc phng phpv k thut tm kim vi s h tr ca thng tin ph gii bi ton mt cch c hiu qu.- Cc ngn ng v Tr tu nhn to: x l cc tri thc ngi ta khng ch s dng cc ngn ng lp trnh dng cho cc x l d liu s, m cn c ngn ng khc. Cc ngn ng chuyn dng ny cho php lu tr v x lthngtinkhiu.MtsngnngcnhiungibitnlIPL.V,LISP, PROLOG.- L thuyt thhintri thcv hchuyn gia: Tr tu nhnto l khoahc v th hin v s dng tri thc. Mng ng ngha, lc , logic v t, khunglccphngphpthhintri thcthngdng.Vicgnlin cch th hin v s dng tri thc l c s hnh thnh h chuyn gia.- L thuytnhn dngv xltingni:Giai onphttrinuca Tr tu nhn to gn vi l thuyt nhn dng. Cc phng php nhn dng chnh gm:nhndng hnh hc, nhn dng dng tm l hc,nhndng theo phng php hm th, dng my nhndng. ngdng ca phngphp ny trong vic nhn dng ch vit, m thanh.- Ngimy:Cuinhngnm70,ngimytrongcngnghip t c nhiu tin b. Ngimy c b phncm nhnv cc c ch hot 5ng cni ghptheo siu khin thng minh. Khoahc v c hc v Tr tu nhn to c tch hp trong khoa hc ngi my. - Tm l hc x l thng tin : Cc kt qu nghin cu ca tm l hc gip Tr tu nhn to xydng ccc ch trlitheo hnh vi, c thc; n gip cho vic thc hin cc suy din mang tnh ngi.- Ngoi ra, x l danh sch, k thut quy, k thut quay lui v x l c php hnh thc l nhng k thut c bn ca tin hc truyn thng c lin quan trc tip n Tr tu nhn to.2. Lch s pht trin ca Tr Tu Nhn To.Lch s ca Trtu nhn tocho thyngnh khoa hcny c nhiukt qu ng ghi nhn. Theo cc mc pht trin, ngi ta thy Tr tu nhn to c sinh ra t nhng nm 50vi cc s kin sau: Turing c coi l ngi khaisinhngnh Tr tu nhntobi pht hin ca ng v my tnh c th lu tr chng trnh v d liu. Thng 8/1956 J.Mc Carthy, M. Minsky, A. Newell, Shannon. Simon ,a ra khi nim tr tu nhn to. Vo khongnm1960tiihcMIT(MassachussetsInstitureof Technology) ngn ngLISPrai,ph hpviccnhucuxlc trng ca tr tu nhn to - l ngn ng lp trnh u tin dng cho trtu nhn to. ThutngTrtunhntocdng utin vonm 1961cngti MIT. Nhng nm 60 l giai on lc quan cao v kh nng lm cho my tnhbit suy ngh. Trong giai on ny ngi ta c chng kin my chic u tin v cc chng trnh chng minh nh l t ng. 6C th:1961: Chng trnh tnh tch phn bt nh1963: Cc chng trnh Heuristics: Chng trnh chngminhcc nhlhnhhckhnggianctnltngt,chngtrnhchi cca Samuel.1964: Chng trnh giiphng trnh is s cp,chng trnhtr gip ELIZA (c kh nng lm vic ging nh mt chuyn gia phn tich tml).1966: Chng trnh phn tch v tng hp ting ni1968: Chng trnh iu khin ngi my (Robot) theo n Mt tay, chng trnh hc ni. Vo nhng nm 60, do gii hn kh nng ca cc thit b, b nh v c bit l yu t thi gian thc hin nn c s kh khn trong vic tng qut ho cc kt qu c th vo trong mt chng trnh mm do thng minh. Vo nhngnm 70,my tnhvibnhlnv tctnh ton nhanhnhng cc phng php tip cn Trtu nhntoc vn thtbi (do s bng n t hp trong qu trnh tm kim li gii cc bi ton t ra). Vo cui nhngnm70mtvi ktqunh xlngnngtnhin,biu din tri thc v gii quyt vn . Nhng kt qu to iu kin cho sn phmthng mi u tin caTrtunhn to rai l H chuyn gia, c em p dngtrong cc lnh vc khcnhau (H chuyngia l mt phn mmmytnh cha cc thng tin v tri thcv mtlnh vc cthno , c khnnggiiquytnhngyu cu cangi s dngtrongmt mc no , mttrnh nh mtchuyn gia conngi c kinh nghim kh lu nm). Mt s kin quan trng vo nhng nm 70 l s ra i ngn ng Prolog, tng t LISP nhng n c c s d liu i km.7 Vo nhngnm 80,th trngccsnphm dn dng c kh nhiu sn phm trnh cao nh: my git, my nh,... s dng Tr tu nhn to. Cc h thng nhn dng v x l nh, ting ni. Nhng nm 90, cc nghin cu nhm vo ci t thnh phn thng minh trong cc h thng thng tin, gi chung l ci t tr tu nhn to, lm rhn cc ngnh ca khoa hc Tr tu nhn to v tin hnh cc nghin cu mi, cbit l nghin cuvc chsuyl, v Trtunhnto phnto, v cc m hnh tng tc.Nhng c trng ca Tr tu nhn to Tr tu nhn toxlthng tin theo trt t k hiu. Ccthng tingm: khi nim, lut, cc i tng ? dng cho suy l. Khi nim c bn trong Tr tu nhn to l s th hin, suy l, nhn bit, vic hc v hthng cs tri thc. Phng php may ri hay c dng trong Tr tu nhn to. Phng phpny cho php gii hailp bi ton kh. Th nhtl nhng bi ton chac thut gii(bi ton nhnbit,ra quytnh).Th hail cc bi ton c thut gii nhng phc tp ln ( chng hn bi ton chi c). Tr tu nhn toxt n nhng thng tin khng y , khng chnh xc, c v mu thun. Tuy vy, cc kt qu ca Tr tu nhn to l c th. Vic tng tc ngi- my i i vi nhn bit t ng l cn thit trong Tr tu nhn to. Cc bi ton nhn dng l v d v yu cu ny. Tr tu nhn to lin quan n nhiu lnh vc, nh cc k thut mi, logic hc,khoahcnhnbit,ngnnghc,khoa hcvtchc,thnkinh hc. Tr tu nhn to cn nm trong cc lnh vc nghin cu nng cao, cc n nghin cu quan trng.83. Mt s vn Tr tu Nhn to quan tm.Nhng vn chung Khoa hc Trtu nhn to lin quan n cm gic, tri gic v c qu trnh tduy thng qua cc hnh vi, giao tip.Ncccnhhngnghin cu,ng dng sau: 1-Tm v nghin cuccthtcgipconngitinhnh cc hotng sng to.Cngvicsngtocthchintrn m hnh theo cutrc,chc nng v s dng cng ngh thng tin.2- Dng ngn ng t nhin. Trc ht l ngn ng c dng th hin tri thc, tip thu v chuyn ho sang dng c th x l c. 3- Hnh thcho cc khacnh, cc hnh vi lin quan n Trtu nhnto. Do vy c th xy dng cc bi ton mang tnh ngi v thng minh.Cc hotnglntrong Trtunhntobaogm: chngminhnhl, xl ngnngtnhin, hiutingni,phntchnhvhnh, ngimyvh chuyn gia. V ci t h thng, khuynh hnghin ti ca Trtu nhn to lci tcc h Tr tu nhnto trongcc hthng khc, c bit l trong cc h thng tin hc.Nhng vn cha c gii quyt trong Tr tu nhn to Nhngthnh tu nghin cuv ngdngcck thut Trtunhnto khngnhtnhthctincacc dnxydngmytnhckhnngsuy ngh.Tuyvytrongmt s phmvi, my tnh cn thua xa so vihotng ca h thn kinh con ngi: Skhc nhau trong hot ng gia my tnh v b no con ngi, iu nyth hin u thca mytnh so vib no ngi v kh nng tnh tonrt ln (nht l trong cc chng trnh x l d liu ln). X l song song: mc d cng ngh in t hin i cho php xy dng cc baxl,songmytnhkhngthhotngsongsongnhbnoconngi c. 9Kh nng din gii: con ngi c th xem xt cng mt vn theo nhng phng php khc nhau, tdin giitheocchdhiunht.Ngcli, s linh hot ny khng th m phng c trong cc h thng Tr tu nhn to.Lgic rircv tnh lin tc: mtthch lnvicchthngTrtu nhn to l kh nng kt hp cc phng php x l thng tin trong mi trng lin tc vi cc thao tc x l thng tin ri rc. Khnnghc:mcdhinnaymytnhcnhiutnhnngcaonhngcngkhngthmphng chontonkhnnghcgingbnoconngi. Khnngttchc:cho tinay,ngitacha thtolpccch thng Tr tu nhn to c kh nng t t chc, t iu khin hot ng ca n thch nghi vi mi trng.Nhng vn t ra trong tng lai ca Tr tu nhn to.Trongtnglai,nhngnghincuv ngdngcaTrtunhntotp trung vo cc vn ln sau:Nghin cuv th nghim cc mng Neuron, cc h thng Trtu nhn to m phng chc nng hot ng ca b no vi cc kh nng hc, t t chc, t thch nghi, tng qut ho, x l song song, c kh nng din gii, x l thng tin lin tc v ri rc. Nghin cuv tolpcchthngcgiaotipthnthingiangivmy trn c s nghin cu nhn thc my, thu thp v x l tri thc, x l thng tin hnh nh, ting ni. Nghin cu cc phng php biu din tri thc v cc phng php suy din thngminh, ccphngphpgiiquytvnivinhngbi tonph thuc khng gian, thi gian.Ngynay, thgiiangchuynmnhtrongnhngnghincuvTrtu nhn to. Chcchn rngmy tnh vi trtu nh con ngi s tc ng mnh n cuc sng x hi.104. Cc khi nim c bn:Tr tucon ngi (HumanIntelligence): Cho nnayc haikhinim vtr tu con ngi c chp nhn v s dng nhiu nht, l: Khi nim tr tu theo quan im ca TuringTr tul nhngg c thnhgi c thngquacc trcnghim thng minh Khi nim tr tu a ra trong t in bch khoa ton th:Tr tu l kh nng:Phnngmtcchthchhpnhngtnh hungmithngquahiuchnh hnh vi mt cch thch ng.Hiur nhngmilin hqualicaccskincathgiibn ngoinhm a ra nhng hnh ng ph hp t ti mt mc ch no .Nhngnghin cucc chuyn gia tm l hcnhnthcchrarngqutrnhhot ng tr tu ca con ngi bao gm 4 thao tc c bn:1- Xc nh tp ch (goals).2- Thu thp ccs kin (facts)v cc lut suy din(inferencerules) t c ch t ra.3- Thu gn (pruning) qu trnh suy lunnhm xc nhtp ccsuy din c th s dng c.4- p dng cc c ch suy din cth (inference mechanisms) a ccs kin ban u i n ch.Tr tumy: cng khngcmt nhnghatng quat, nhng cngc th nucc c trng chnh:1- Kh nng hc.2- Kh nng m phng hnh vi ca con ngi.3- Kh nng tru tng ho, tng qut ho v suy din .4- Kh nng t gii thch hnh vi.5- Kh nng thch nghi tnh hung mi k c thu np tri thc v d liu.116- Kh nng x l cc biu din hnh thc nh cc k hiu tng trng.7- Kh nng s dng tri thc heuristic.8- Kh nng x l cc thng tin khng y , khng chnh xc5. Mt s chuyn ngnh ca Tr tu nhn to:1. Cc phng php tm kim li gii.2. H chuyn gia3. My nhn v ngn ng.4. L thuyt nhn dng.5. Cc m hnh thn kinh.6. Ngi my.. . .12Chng 1BIU DIN BI TONTRONG KHNG GIAN TRNG THI1. t vn .Khi giiquytbi ton bngphng php tm kim,trchttaphixc nh khng gian tm kim bao gmtt c cc itngtrn thchin vic tm kim. Mt phng php biu din vn ph hp l s dngcc khi nim trng thi (state) v ton t (operator).Phng php gii quyt vn da trn khi nim trng thi v ton t c gi l cch tip cn gii quyt vn nh khng gian trng thi.2. M t trng thiGii bi ton trong khng gian trng thi, trc ht phi xc nh dng m t trng thi bi ton sao cho bi ton tr nn n gin hn, ph hp bncht vt l cabi ton (C thsdngccxukhiu,vct, mnghaichiu,cy, danh sch).Mi trng thi chnh l mi hnh trng ca bi ton, cc tnh trng ban u vtnh trng cui ca bi ton gi l trng thi u v trng thi cui.V d 1. Bi ton ong ncCho 2 bnh c dung tch ln ltl m v n (lit). Vingunnc khng hnch, dng 2 bnh trn ong klitnc.Khngmt tnh tngqutc th gi thit k akl,ik, j l- Trng thi u ca bi ton l ma trn- Trng thi cui l ma trnC th pht biu dng tng qut ca bi ton ny (Tr chi n2-1 s)|||.|

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\|5 6 74 0 83 2 114V d 3. Bi ton thp H Ni Cho ba cc 1, 2, 3. cc 1 ban uc n a sp xp theo th t to dn tdi ln trn. Hy dch chuyn n a sang cc th3 sao cho:- Mi ln ch chuyn mt a.- Trong mi cc khng cho php a to nm trn a nh hn.Bi ton xc nhkhibitctngaangnmccno. Hay ni cchkhc, c hai cch xc nh:1-Cc1hin ang chanhngano? Cc2hinangchanhnga no? V cc 3 ang cha nhng a no.2- a ln th i hin ang nm cc no? ( i = 1 .. n )Nh vy cch m t trng thi bi ton khng duy nht, vn l chn cch m t no t c mc ch d dng nht. Theo trn, vi cchthnht ta phidng 3 danh sch ngv s atrn mi cc l khc nhau trong tng thi im khc nhau. Cch thhai,nhn qua th kh m t nhng da vo khi nimv bc th t trong ton hc, cch ny m t bi ton hiu qu hn. Tht vy, nu gi xi l cc cha a ln th i, trong xie{1, 2, 3}, ie{1 ..n}. Khi b c th t (x1, x2, .. ,xn) c th dng lm dng m t trng thi ang xt ca bi ton. Vi cch m t ny,Trng thi u l (1,1,. . .,1)Trng thi cui l (3,3,. . .,3)3. Ton t chuyn trng thi.Ton t chuyn trng thi thc cht l cc php bin i a t trng thi nysang trng thi khc. C hai cch dng biu din cc ton t:- Biudinnhmthm xc nhtrn tpcctrngthi v nhngitr cng trong tp ny.- Biudindi dngcc quytcsn xut S?Ac ngha l nuctrng thi S th c th a n trng thi A.15V d 1. Bi ton ong ncCc thao tc s dng chuyn trng thi ny sang trng thi khc gm: y mt bnh, ht nc trong mt bnh ra ngoi, nc t bnh ny sangbnh khc. Nh vy, nu trng thi angxt l (x,y) th cc trng thi k tip c th chuyn n s l:(m,y)(x,n)(0,y)(x,0)(x,y) (0, x+ y) nu x+y < = n(x+y -n,n) nu x+y > n(x+ y,0) nu x+y < = m(m, x+y-m) nu x+y > mV d 2. Tr chi 8 sCc thao tc chuyntrngthitng ngvivicchuyntrngsang phi, sang tri, ln, xung nu c th c.- Biu din theo quy tc sn xut:- Biu din theo mt hmGi hm fu l hm biudin choton t chuyn trng ln trn; gi B(B= (bij)) l trngthisaukhidichuyntrngtrngthiA(A=(aij)) ln trn,ngha l: B= fu(A), gi s trng ang v tr (i0, j0) (hay ni cch khc ai0 j0 =0) th hm f c xc nh nh sau:1 3 42 58 7 61 32 5 48 7 61 3 42 5 68 71 3 42 58 7 616aij(i, j) nui0= 1fu(aij) = aijnu(i, j) = (i0-1, j0) v (i, j) = (i0, j0) v i0>1ai0-1, j0nu(i, j) = (i0, j0), i0 >1ai0, j0nu(i, j) = (i0-1, j0), i0 >1Tng t, c th xc nh cc php chuyn trng xung di fd, qua tri fl, quaphi fr nh sau:aij(i, j) nui0= 3fd(aij) = aijnu(i, j) = (i0+1, j0) v (i, j) = (i0, j0) v i0 1aij(i, j) nuj0= 3fr(aij) = aijnu(i, j) = (i0, j0+1) v (i, j) = (i0, j0) v j0< 3ai0-1, j0nu(i, j) = (i0, j0), j0 < 3ai0, j0nu(i, j) = (i0, j0+1), j0 < 3V d 3. Bi ton Thp H Ni vi n=3. Mi trng thi l mt b ba (i, j, k). C cc trng hp nh sau:- Ba a cng nm trn mt cc: (i, i, i)- Hai a cng nm trn mt cc: (i, i, j), (i, j, i), (j, i, i)- Ba a nm trn ba cc phn bit: (i, j, k)17(i, i, i) (i, i, j)(i, i, k)(i, i, j) (i, i, k)(i, k, j)(i, i, i)(i, j, i) (i, j, k)(i, j, j)(i, k, i)(j, i, i) (j, i, j)(j, i, k)(k, i, i)(i, j, k) (i, i, k)(i, j, j)(i, j, i)4. Khng gian trng thi ca bi ton.Kkhng gian trng thi l tp tt c cc trng thi c th c v tp cc ton tca bi ton.Khng gian trng thi l mt b bn, K hiu: K= (T, S, G, F). Trong ,T: tp tt c cc trng thi c th c ca bi tonS: trng thi uG: tp cc trng thi chF: tp cc ton tV d 1. Khng gian trng thi ca bi ton ong nc l b bn T, S, G, F xcinh nh sau:T = { (x,y) / 0 0, m=1: cu Horn c dng: p1. p2...... pnq: gi l lut (rule).Trong cc hchuyn gia, c strithcgm 2phn:tp ccskin(facts) vtp lut (rules).V d1) Ta c cc lut v kinh nghim d bo thi tit:"Chun chun bay thp th ma, bay cao th nng, bay va th rm"a: chun chun bay thp, b: chun chun bay cao, c: chun chun bay vad: tri ma, e: tri nng, f: tri rmlc ta c cc lut sau: a db ec f2) Nhiu nh l trong ton hc c th biu din bi cc lut, v d:Nu tam gic c mt gc bng 600v tam gic c hai cnh bng nhau th tamgic l tam gic u.3. Suy din trn lut sn xut3.1. Khi nimSuy din l qu trnh suy lun da vo cc quy lut cho, thit lp cc thng tin mi t cc thng tin bit. Suy din s s dng tp s kin lm tin . 153Cc phng php suy dindndnchuyntccgithitvccktlun bng cch thm vo gi thit nhng s kin c khng nh ng, da trn 2phng thc:- Modus ponens: A, ABBngha l nu A ng v AB ng th B cng ng- Modus tollens B, ABAngha l nu B sai v bit rng AB ng th A cng sai.Trong qu trnh suy din, ta cn quan tm n cc vn sau:- Xy dng tp lut, cu hi no c chn ngi s dng tr li- Chn qu trnh tm kim nh th no- Thng tin nhn c c nh hng n qu trnh tm kim khng3.2. Bi tonCho tp s kinF={f1, f2,...,fn} v tp lut R={r1, r2,...,rm}. Chng minh tp kt lun G ng.3.3. Cc phng php suy dinQu trnh suy din trong h lut sn xut bao gm 2 phng php c bn: suy din tin v suy din li.a)Suy din tin (lp lun tin - forward chaining hoc forward reasoning)(T tng c bn ca suy din tin l p dng lut suy din Modus Ponens tng qut)L qu trnh suy din bt u t tp s kin bit, rt ra nhng s kin mi v c nh vy cho nkhic c s kin cn chng minh hoc khng c lut no sinh ra cc s kin mi (tp s kin ng l cc i).- Phng phpGi T l tp cc s kin ti thi im ang xt (khi to tp T=F: tp s kin ng ban u ). 154Xt cc lut ri c dng:p1. p2 . ..... pn q v pjeT nj, 1 = ngha lleft (ri) eTth T= T+ right (ri)qu trnh lp li cho nkhi Gc T hoc khng c lut no sinh ra thm s kin mi.- Gii thutProcedure suydientien;BeginT:= F;S:= loc(R, T); { S: l tp lut c dng p1. p2 . ..... pn q sao cho pjeTnj, 1 = }While G .T and S| doBeginr := get(S);T:= T + right(r);R:=R\ {r};S:= loc(R,T);End;If G cT then write (thnh cng)Else write (khng thnh cng);End;V d1) Cho trc tp s kin F={a,b}. S dng cc lut:r1: a cr2: b dr3: c er4: a . d e155r5: b . c fr6: e . f gcn suy ra gr T S Rr1r2r3r4r5r6a, ba, b, ca, b, c, da, b, c, d, ea, b, c, d, ea, b, c, d, e, fa. b, c, d, e, f, gr1, r2, r3r2, r3, r5r3, r4, r5r4, r5r5r6r1, r2, r3, r4, r5, r6r2,...r6r3,..., r6r4, r5, r6r5, r6r6geT nn bi ton c chng minh (g: true)Ch - Qu trnh suy dintin l qu trnh xem xt cc lut,vi milut ta xt phniukin( v tri)tiphn kt lun (vphi)v khi m ttc cc iu kin calut u tho mn th ta suy ra s kintrongphn kt lun. Chnh v l m c tn l suy din tin.- Trong mi bc ca th tc, ngi ta xt mt luttrong tp lut. So snh miiu kin (v tri) ca tp lut vi cc s kin trong c s s kin, nu tt c cc iu kin ca lut c tho mn th s kin trong phn kt luncxemlskincsuyra.nuskinny lskinmi (khng c trong bnhlm vic)th n ca vo bnhlm vic. Qu trnh trn c lp li cho n khi no khng c lut no sinh ra s kin mi.156- Qu trnh suy dintin khngnh hngtigii quyt mt vn noc, khng hngtitm ra cu tr li chomtcuhi no c.Suy din tin ch l qu trnh suy ra cc s kin mi t cc s kin c trong b nh lm vic.b) Suy din li (lp lun li - backward chaining hoc backward reason)L qu trnh xut pht t s kin cn chng minh v thay vo l nhng s kinvtrica1lutcvphil skincnchng minh.Qutrnh nyc thc hin cho n khi a v cc s kin l tp s kin con ca tp s kin gi thit.(Ngha l: a ra kt lun b, ta th tm tt c cc lut c dng: a1. ..... an b, c b, phi a ra cc kt lun a1,...,an. Qu trnh xc nh ai cng tng t nh ivib,nunmtlcno pht hincrngcmtaino khng dnxutctccgithitth quay lui sang cc lutsnxutkhc sinh ra b c dngb1......bm b. Ngcli,nu mi ai u dn xutc gi thit th qu trnh dn xut ra b l ng)- Gii thutGi T l tp cc s kin cn chng minh ti thi im ang xt (khi to T= G, G l tp kt lun).S(p) ={rieR / right(ri) = p} ( l tp cc lut trong R sao cho v phi cha p)Procedure suydienlui (g);BeginT:= {g};If TcF then write (g c chng minh )ElseBeginp:=get(T);If S(p) = {} then write (g khng chng minh c )157ElseFor rieS(p) doBeginT:= T \ right(ri);T:= T + left(ri);For leT \ F do suydienlui(l);End;End;V d1) Cho tp s kin F={p, r}, v tp lut R:r1) p qr2) q . r sChng minh sp r T S(p)sqr2r1sq, rr, pr2rNhn xt- Suy din tin:u im:i)Lm vic tt khi bi ton c bn cht l i thu thp thng tin ri thy iu cn suy dinii) Cho ra khilng lnccthng tin t mtsthng tin banu. N sinh ranhiu thng tin mi.iii) Suy dintin l tipcnltngiviccloibi ton cngii quyt cc nhim v nh lp k hoch, iu hnh, iu khin v din dch.158Nhc im:i)Khng cmnhncrngchcnmt vi thng tin quan trng. H thng hi cc cu hi c th hi m khng bit rng ch mt t cu i n kt lun c.ii) Hthng c thhi c cu hikhng lin quan. C thcccutr li cng quan trngnhng lm ngidng lng tng khi phitrli cc cu chng dnh n ch .- Suy din li:u im:i)Phhpvibi ton aragithuytvliugithuytcnghay khng?ii) Tp trung vo ch cho. N to ramt lotcu hich lin quan n vn ang xt, thun tin i vi ngi dng.iii) Khi suy din mt iu g t thng tin bit , n ch tm trn mt phn ca c s tri thc thch ng i vi bi ton ang xt.iv) Suy dinli cnhgicaotrongccbi ton nhlchnon,d on v tm li.Nhc im:Nhcimcbncaloi suy dinny ln thngtiptheodng suydin thay v ng ra phi dng m sang nhnh khc.- Nh vy, da vo cc u v nhc im ca tng loi suy din m ta nnchnkthut suydinno pdngvo bi ton.Trctin, ta xemxt cc chuyn gia gii n nh th no?. Nu cn thu thp d liu ri mi quytnhsuydincigthtachnsuydintin.cnnuc gi thuyt v cn chng minh ci ch ny th ta dng suy din li.V dMtbcscthhiuhng trm vncthxy ravimtc nhn, nhng vn phi tm hiu hin trng ca bnh nhn, lc cn suy din 159tin.Ngucli bc s hu nh thy c bnh ( v d nh vim hng) th ng tadng suy din li.Bi tp 1.Cho cc biu thc logic mnh ng sau:1) ac2) abf3) (d +b)f i4) h + a + f5) fgh i6) (a + d + c )7) ad ghChng minh hoc bc b mnh i bng phng php suy din tin v suy din liLi gii- Biu din cc biu thc ng cho bng lut sn xut (xc nh tp lut, tp s kin ban u, tp s kin cn chng minh)Qu trnh bin i3) (d+b)f i ((d+b)f )+i (d+b)+f+i (db)+f+i (d+f+i)(b+f+i) (df i )(bfi)4) h + a + f (ha)+f ha f1) (a + d + c ) (ac)+d ac d2) ad gh ) (ad)+(gh) ) ((ad)+g) ((ad)+h) (ad g)(ad h)Tp s kin F={a, c}, tp s kin cn chng minh G={i}Tp lut R:r1) abf r5) fgh ir2) (dfi ) r6) ac dr3) (bfi ) r7) ad gr4) ha f r8) ad h160- Suy din tin (tin hnh lp bng sau)r T S Rr6r7r8r4r2a, ca, c, da, c, d, ga, c, d, g, ha, c, d, g, h, fa, c, d, g, h, f, ir6r7, r8r8r4r2, r5r1, r2, r3, r4, r5, r6, r7,r8r1,...r5,r7, r8r1,...r5, r8r1,...r5r1, r2, r3,r5(trong : r: l lut ang xt, T: tp s kin ng ti thi im ang xt, S: tp cc lut c dng cc mnh v tri thuc T. R l tp lut ti thi im ang xt)V ieT (l tp s kin ng). Vy i c chng minh- Suy din li (tin hnh lp bng sau)p r T S(p)ifbquay luifhdr2r1r2r8r6id, fd, bdd, hdCr2,r3, r5r1, r2Cr2r8r6Vy i c chng minh161Bi tp 2. Cho c s tri thc c biu din bng cc biu thc logic ng sau1) pt a 5) p t2) qt s 6) apq c3) pq b 7)bc t4) b st 8) pqBiu din tri thc cho di dng lut sn xut v dng phng php suy din tin v suy din li chng minh hoc bc b s kin s1.Bi tp 3. Cho c s tri thc c biu din bng cc biu thc logic ng sau1) (a+c)b f2) e +f + a3) gfh i4) (e+ f)b gi5) (a+ e +c)abcDng phng php suy din tin v suy din li chng minh hoc bc b s kin i1.Bi tp 4.. Cho c s tri thc c biu din bng cc biu thc logic ng sau1) efh2) a + g + d3) h + c + d4) af bg5) ke d6) (ef a )(c+ e +f )- Biu din tri thc cho di dng lut sn xut - Dng phng php suy din tin chng minh s kin d1 ng. Cho bit cc lut d tha trong vt suy din162Bi tp 5.. Trong mtlphc,cmtnhmhcsinhgm10bnctn ln lt l: A, B, C, D, E, F, G, H, I v J. Gia cc bn hc sinh c mi quan h gi l quan h nh hng. V d: nu ta vit AB>C th c ngha l hai bn ng thi cng thuyt phc bn C tham gia mt hot ng no . Gi s ban u c bn bn E, F, H, I tham gia d thi sn phm phn mm do nh trng t chc vta cng bit c rng:1) ACH>B2) BH>ACD3) ABCI>BDI4) ADEI>BCG5) CGI>AJE6) H>BCHy dng phng php suy din tin chng minh rng c 10 bn trong nhm trn u tham gia d thi sn phm phn mm.