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tlA IMOBlii TfNH niM Bfi TRi GlAl NIA CHO IHA B!NH B IEN BANG OroiHAr Ml Ns«G mr , FMNiilNi Ur TdM TAT Tmng ly biuyit mi, dS cd mCt si dng binh nghiin cOu iy blQ d i nhin dugc due bin viic nghiin cOu[.]
tlA-IMOBlii- TfNH niM Bfi TRi GlAl NIA CHO IHA B!NH B I E N B A N G OroiHAr Ml Ns«G m r , FMNiilNi Ur- TdM TAT Tmng ly biuyit mi, dS cd mCt si dng binh nghiin cOu iy blQ d i nhin dugc due bin viic nghiin cO dc bnh chit da bi gUi mi Bii vdi de hi thing dng dgi^, viic xic dfnh ehhih xic ,AV,A% hrong ftng V^, = X-V, + U-'X* 'i>0 ChoMldv(nhdmttiy>vdiddnv|ldVOitM,= TTnh dftng din cfta ttift tgc ndy dvpc dva ttin {(i.m.»)|m,M.i.96B)ij{E.8}.diOiiyMxeA% duprc gpi Bed mpt phdn tich dnhusau: ttin X niu xed Oii biiu diin dvdi dpng x = x,.Xy.j ddn VI z e ({a) + {a E 1) I IEB )) suy y,.y, y vi id vd cd chua phin td zero l i vd p: A* -> Mi i j o i - r - i I i ' i T ^ , ' 'ã ằj-^s5i-ôrr=* xiyra^^Sjf^^J^r^'^"^ i2J tnCii-TiiMidiVl z'€ V„, ttieo gB Oiiit quy nap Oil z"ttidawiu Chftng minh (=>} Ta chftng minh quy npp 1ft Oieo d nhu sau: ttiftc (2) Khi dd tin tai m ^ Xg x, x,^, yo.y, - GB sft, vdi d = 0, la phil chftng mlnh U « g ; y X cho v x , x,.,^'- = y,.y, y vfti x, vdV,ô0 '* ãyrrC) (a) Niu X, = y,.y, y,.z vd ^ y , , vdi naO, x Hdn z vdo hai vi v i phla bin phii cia biiu yo.yi y„ E X Ta phil chftng minh zeU^ ttiftc (4), suy re Thit viy, vfti x, = y y y z E X, suy z E x,ji, HJ,.X = x„ji, x^,J?.z = y„.y, y„.z vfti (Yrx H«y,xxi.yp«X Chpnm = 0, kWditac6x,= y,.z.TheogBô(Jt Viy Ơz e U,ttioaWiuttiftc(1) ã Niu z a (YT(V„X) KW d i sd tin tpi O-tft y x,iiy„, suyraz>(l,e, i),vdiiEB DodiZE ( V „ X - { e ) - { ( i , E , i ) | i E B ) ) = U„,vdiV, = Y• = yo'-y,' - y." e x* cho (b) Niu x,x = y„.y, y , vd x,»y,, vdi neo, x, z' = y,'.yi' y,'.z6V.,x.(5) y„ E X Ta phdi chftng minh zeV, Dot E V^^ quy vi trudng hpp vfta xit d trdn, y(,.y, suyretin tpi sv phin Och: Thit viy, vdi ^.z = y y y„ s Y", suy z E x,.x, X = y,.y, y X vfti x , » y, x, y ^ X-'Y- X.(e) Chpn m = 0, dd ta ed ^.z = yo.Theo gBi ttiiit Thay z" tft (5) vdo (6) suyra:Xg.x, x = yg.y, Xo^yg, s u y r a z e v d z ( l , e , i),vdlJEB DodiZE (X-V, - (a) - {(i, E, i) 11 B B )) £ V,, vdi V, = Yô -y.-y,'yi'-y,'-z.vftix.ằy^x,.y yã e x - Gid sft, U,, V„, dftng vdi k == d, Ta ehftng mlnti Viy, Vz E U Olda biiuttiftc(1) (b) Gii sft V,^, * Ta phii chftng minh, vdi U v i V„, cftng dftng vfti k < d NghTa li, Vz a U,thi8 biiu ttiftc (10) vd Vz E V „ , Oiia biiu thftc (11), mpi O-tft z e V„„, Bn tpi m a 0, X., X, x., y^, y, (a) GB sft, vdi mpi 0-tt> z e A%, m i 0, x., y,6 X dio x,.x, x,.z = y,.y, y„, vdi x,»y, Thit viy Iiy z E V „ , d i ed hai khd ndng xiy = d hope X c i dp tti vd hpn Theo gii Biiit, X khing ed dp tti giii md hftu hpn d Khi di Vm i 0, v v x, v y«.yi y , E X, vz E A%, ta cd biiu ttiftc: v ^ - V ^ = yi,y,.y vdi Thed cdch xdc djnh U, v i V „ d trin, suy z E V „ , miu ttiuin Viy X cd dp tti gidl mi hftu hpn Otomal xdc d|nh dp t r i gUI m l Tft ttift tgc xdc djnh dp tti gidi mi cia mit 0-ngdn ngft ft ttin, chftng ta ed nhin x i t Cic tip V„ U, si nhin dvpc sau mil bufte tinh todn nhft dp dgng hftu han cde phdp u, r\ -, cde phip cil bii, phdi Niu X B O-ngdn ngft chlnh quy Oil ttieo kit qud Wnh diin, si cdc tip V„,, U, Oida bdi todn eiu v| nhdm p: A*„ - • P, vdi P B mftt vj nhdm hftu hpn, nghTa B s i cde tip V„,, U, khdng vupt qud s i tip eon eOa P (bing 2i^ Sau diy chftng ta nhie Ipl mit si kit quittongly ttiuyit mi B CO sft xdy dpng ohimat hftu han xdc ^nh d i tti glil mi cua mpt O-ngin ngft Chlnh quy b E B, »'(x) = (ot(x), m) = (h, P(x)) E B' nhu viy »'CX)sB' Ngwc Ipi, vdiy E ^'{B') c A%, 9'(y) E B' ip'(y) = (»(y) Ky)) = (b, n) E B' Tft dd ta cd ttii viit p'(B') = X = qi-'(B'nP) B - ' B ' r ^ P c P p'(Cl = Y = pr p B todn eiu suy p(u) = •PXU) DO dd ip: A * -> P Oidi ttida ding ttidi ed X vd Y Tft Bi d i ta ed Bd di sau ddy B i d i Cho X.Y e A% Id cde O-ngin ngft chinh quy Niu X Y cftng Oiia bfti toin ciu vj nhdm ip: A-0-»P vfti P B mpt vj nhdm hftu hpn Oil ip eDng Oida mpl tE^p q dvpc gpi B dvftng di ttidnh cdng niu q E T Dinh nghla Cho otomat = (Q A q^ T) dvpc xdc djnh bfti X Mit dvdng di dgng P: q„ = (1, V, U, is_u) -> q = (k+1, V, U', is_ul, k 0, dvpc gpi BttidnhcingttongA Khi dd, gid cua dvdng P, ky hiiu B Val(P), vfti Val(P) = k Minh d i sau diy khing djnh Onh dftng din cia Minh d i Cho otomat A = (Q A qg, T) d w c xic djnh bdi X nhv ttin ^ B tip tit ei ede dvftng di ttidnh cingttongA Khi dd X cd dp tti giii mi hftu hpn d, dvpc xdc djnh bdi: d = Min{ k I k = Val(P), P E P> Chftng mlnh Xdt P E P, d = Val(P) dd Vd+1 =• (ttiee gid ttiiit), suy d B dp tti cia X (Oieo Minh di 1) Sau ddy ta si chftng mlnh d B d i tti giii mi dia X ttil d phil B gB ciia dudng dl ttiinh cing ngin nhitttongA Thit viy, gii sft niu cd d' z''e U,, -»MsaochoL = p-''(N),vdiNcMndodd saocho ei»l» l> (xam PS Cho t c A'' Khi dd cdc "-^ ° ^M - ^i f''^'''' »« Y = X(3) diiu Win sau diy... diim bit kjr, otomatftttpngttidiq = (1, V, U, is_u), tCry Oiupc vdo gB tt) eft Och lOy Is u md otomat chuyin sang trpngttidimdi q'' = (1'', V", U'' is.u") Oieo hai ttvdng hpp: B i d i Cho hai O-ngin... dd, suy z e V,-''X hcic saocho: z a (Yr(V,-''X) z" = xz E V,(7) VI z'' e V, Oieo gB ttiiit quy npp Oil z'' ttiia biiu ttifte (2) Khi di tin tpi m £ x, x, x,.,, y,,y, y„e X cho x,.x, x^,t = y,.y,