Motifs Séquentiels Flous : Un Peu, Beaucoup, Passionnément

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(1)Motifs Séquentiels Flous : Un Peu, Beaucoup, Passionnément Céline Fiot, Anne Laurent, Maguelonne Teisseire. To cite this version: Céline Fiot, Anne Laurent, Maguelonne Teisseire. Motifs Séquentiels Flous : Un Peu, Beaucoup, Passionnément. EGC: Extraction et Gestion des Connaissances, Jan 2005, Paris, France. pp.507-518. �lirmm-00106089�. HAL Id: lirmm-00106089 https://hal-lirmm.ccsd.cnrs.fr/lirmm-00106089 Submitted on 21 Sep 2019. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(8) yd6F;:<C?deA D,6F61;N0323M69;ý MNB :< C?6r MW~ S=K6Fd?4?B<MN6FD(u l¼6Fsgfz76F03616kl4?d705:K:<056<C JK=t25GC7C746k]7?6Fm:KJ<C7DE/k6\]7MN:<6\4GÈ?;m C747de6:KC7JKDU/F470369/1DEMNB<:<03C?2|MNMWB`S;N61254?:<MN4$6Fl*]761z?M036:<edy:</FD C B ;E6FC7D M 0|B<6;MEMW]f2|G6\C7È?61mM1^ m ü4?k:<4 DEl~ :<6\4?pMN472|:K]fDNFlDE6n647;Nÿ DE:`25; B<B`47lJ<C7l0|B`6F254GDE;{6[05B"6[MR;4?/F0µ JK:<B`dy;N/F25D :<B 4P;E=6FC70µ D234Gz7;E256F4?D B`MW256 DN~ 6U;N25]:<4234G;N6F61;{DEMN0µ6 C7~ 47;N2525:<:<44PmUÄ A :<dy/FD B ;E6FC7~ D :<C;WS ]P UC74?JK23/F:K474å/1m,DEAB<Ä 03 2|:KMNde/\/1B<DECB`;N~61B<C7MD 4fSÛB`25:KDNC6Km ;WS ~ :K47:<DEl6Ümt ¿,~ :<:<4?Ce:<MDE47l:`6;E6F;NDEDE:<254?B<M47J<C?05pB<DE2361DEMN6[dPm 6[MR;n00 :K :Kdede/1/1DEDEB`B`;N;N6F6FC?C?D D$z725p4?DE61B`MN25DEdP6 m ;; E23B`61z74725A470 25B61ME4KB`4G;;¯ ;N~ :K6FC?;M\6F4e036[MW[Mk61r l*/103z7/1l0556<u 6F= 4G~ ;E6@Ms[GýedyC7u:<2esC7deþ Dÿ61Cf0561;(s MEÿÀFG;Nv C7DE6F6,0|M\DN/[ÿ 03B`6052 ]fMNýy/,61u J<MNDE6F6[/05MR:<;]4{ 03B`G6d?C?d?47B B`:<;EDNDNl;N6 61z7~4?DE:<B`6l4 ]~df6* ; /FB`056[/FJ<MRl6[;9M6F474GÄe:K; W4MY[4tGC7C70,24 µB`~ bKd?:Kkd?lB`d7DN4 SS ~MN6F:<C?4?23MN02|m]f.(/FD 6 B`4G~ :<;lMN6FdfC?; 03B`61JKl661614GMW;;\05B<61d7Mde/F610503/F/lÏE6FÐ 4G,;EMÑ ]fÍ :KK4GÌ ;ÌF056Î ]f61J<DE^G/$] B`4 d7deMW:KB`lDN;Nl6F4eB<B`4K4 ;k~ 6036[Mk]f/1]fd?61B<J<MEDEMW/16$M,C7]P4 B<d7~ d?6FDNB`;EDNB`;N256F4 S 4e]76FB`J<4 DE~ /16@M]f]P6 B<~ d7?d?BKB`GDNC7;N6,614?/FB`05/F4 l~ 6614KMW;[C7mtdy.(/F6DE256F~ C7:<D lMdf¯; B`C7J<4c6MW6[61MRC7;U23B`0Pd7]7dy:<6F470547/ /K=?B`d?deÍ 61W03Ï / Ð ,Ñ Í KÍ WÌÏ Ð_G,Ñ Í4{KMWÌ :KFlÌlÎ B<4K;(m 036[M æçµæ ï òÜö ì fî Xò)òKë Uó@ï õ 7îRï ùNò .(e<B<.(ÍG:KC7Ì 4?6IMN254f]fSÌ/1C7DNd7:K054?6Ì M; IÄ~ 0µ:K 25C7DN]7DE476F616k4GMN;Ndez?23:KieB<4?MNB`6,]4G;DE¯)6F]fJ<C7CDE:<47C?~605d?2361;NB`D 4K4GB`;[;4?=0µME056FBB%4e~ ;NMW]72561B :<l*;E46z7605]76@; 6]f~ 6[0:K M(B4?~BMW?2|~ MWB`?;N;6IB ; B`M61254}4?DN/[MNC7B`20542KMNC?/1;N6MDE25ded70B`036F6FD(4?; MN]76F61lM z7~WÏ0503236n61Ì4K]f; 6[MFM m d?ºfDN:<:f23; ]fC723;EM*p23;N6FlM B ~ 76F;N/[M0 61m 4?MN6Fl*z?036*]761M meT@4 ÛÌ FÌ 61MW;@C74I614?MN6Fl*z?036*]P 23;N61lMk47:K4 C?MN/12|47]fG66*C761034?2|4 MW:`;N~ ;N66 / :<~ :<D ]fl:<de4?:G47MW/F/16K69=e]f476me:KOÛ4 0M123;N2|B<]f61J<l6<23=P;kM1]Pm ] 23 ;NC76147l6MNDN661; d7M9DN47/[MW:<61;N4G/F;E6 B ;E23:K4n47:<4c:KDE]f:KmP47T,47/1476<6 meT@476 FÎ?Ì FÎ?Ï Ì Ì@ÏE6[ÌMR;9C7614?MW6; T@M1 23470P6(6FMNgf/125MWG;NC76614]f~6[6M6F4G;N256FD M 6[MR; C?476MN:<C?MWSMN/1;NG6FC70|M,614 G~ C766 ]P C74?6B`Cf;EDN6(MW/[KC?6F4 ~ 6 LMN/1:<GCeC7M614 0561~ M6B]f~6?]fB :K; 47M47]/1 61C7M4)]flC ÀF~ l052 6F6 4G;1~ m`052 T@6F4G4 ;~ MN0325:<6F4G4G;; DNX61Î[J<Ñ<DEÑ?:<Ð C7dyÛÌ/1MC7476F;6MN;N/1DE25G/1C7M961d?4 B<~ 6D*]7B`MN2;N6<m61OÛMW05;M 23~4 :<~ 4e05C?MR;EMW62;EC7]76FB<4G4?;*M0|0|BB m MNX/1Î[GÑKC7Ñ761Ð 4 e~ 6U]]f C76(47]76@:<MN47/147G/1C76161M4 ]f~ 66 ~ 6 61~MW03;256F056,4G;Ude:KC761D MW~ ;6F4GC7; 4?B`6(J<MN6:<]fC?6[MWM SMN~ /105G2 6FC74G61;E4 M~ G6C7]72y6MW0|C?B@d7MNde/1:KGDWC7;E6F6F44G;~ 6(]7mG6(ºt:K]f2:K; 4747/F6[MEm[A 6 05 6kÂMNÌ C7d7]7dy:<:<4GDN;;03l6MN2547C723d7ldyC7:<lDN;i761MWgf;@/,MWd?C7B`dyD(/F0µDE 25Cf6F;EC723D,052 ME¯ B ;E6FC7D[=<C?476@MN/16[GMRC7;,6FC74 4?~ 66@GC7F2 Î? Ì /FDEÏE23i?Ì 6036kFMWÎ?C7Ì d?deÌF:Km DW;l254725l*C7l æç ï òÜö ì fî Xò)òKë Uó@ï õ 7îRï ùNò%úkìókò 05]P61 M\Cf;EGOÛ234GC?052|;EB`MWC7614G2D ;E;E22 ~;E 6[/16FMM@lMW]76F:K6 4GC?;[~MR=?S6FdeBK4eK:KMWC?C7616Dl*2z7:<;Ez7056F61lÊ;NM(6F4??:<23:KD{CC?]fMd76[DNdeM:f:K]fC7lC?D2:`;k0|;EB2B oM{~DE76 MN~6/1?;EG/6FC7D 6F~61474G6\;Nd7256F]703Ce0|6MMW25MW?6F/[C7:<KC?D C?M@M16F=4MN:<25~ 0@Ce61MUMRMFS op6FB`DE4?JK/1MN2G;{6FC7l]f6F4Gz76c;E056161deMM1B`m ?DN;N:K23;NC?25Mk:<47d747C7612|MD /F254G;N;N/{61ADDE/1BB`B<d705032|DE61MN6F/FMl6?25d?:KFC?B`DED6M1myd7 .(,DE:<6F:Kdydy476F:KJc4?MN2]?6;E;B`23:K4GB`4I;10=em3]=de b`C?:KÈ<C747È?D,6Y[lB<mPd7234?d7AP23DE6Fl: C?~ 2|D?MW616d7D,DE]f:<036*6*dy:K47DE6MN:<2~ l;E723:K61z74D DN~ 6?6[]P6MR;* 23]f;Nze6*61B<llMN/FM,:`6?;E2MW:<oC?M\CeDMMN/1C7lG4wC7B`6F47]f4G25/ d7;E~ 23C7:<6105C?05/1M,d?M1?=7B`JK:<250 6C?M@Mk476F4B6 ;E~ :<:<Cf4?;EMN696FD 05 B614Gz?;1BK=tMW6de:KC7d?DB`D ~ ?BKS K~ C?:K6\l23d7;N;E61B`lnJK=?6[Gm C7690369MN:<C?MWS6F4?MN6Flz7036k?:KCn]76 ~ B`D ]f254?B`0056d703CeM/F056 /\dy:<C?D . Grand. P etit.

(9)

(10). > µA∩B (x) = >(µA (x),. µB (x)) ⊥. ⊥ µA∪B (x) = ⊥(µA (x), µB (x)).

(11) . . 54 76. 8. ⊥. ,%-'.# /. "! $# 0%-'.# /. >. . "! $# &% ')()(+*. 3. >. "! $# 1% ')()(2*. 94. DB '>= 7/ = ! DCE')! ?F% ?!+G t. ;:<'>=/ ?(@' ?AB!C. I = {i1 , i2 , ..., im } (i1 i2 . . . ik ). H')! DF% D!. items. I%?*KJ DA A /<%D*KJ DA. < s1 s2 ...sp >. n < s1 s2 ...sp > l1 < l2 < ...lj ... < ln. L%. %. s2 ⊆ s. < s01 s02 ...s0m > sp ⊆ s0ln. s0l2 , ...,. s. s. M-!. s. s. 7'>N $N Q. s1 ⊆. M-!. s0l1 ,. s. 3. minSupp. 54 76. 8. minSupp. F%?*KJ DA 9OKMP*KJ DA !. 94. >R. Σ. 509. RNTI-E-3.

(12) ;EC774/F:Kop:<DN.(DE2|G7lC76FB`46*052 ]fMN6FlCc;6kd7B`DE06Fm5:<;,=Uz?]fb`03161ÈKlMÈ7YK476· :<MN;E,B<B`4?C;N25M,:<6B`4?;n05MJ<B`:KB`0DNlm323=;Nz7?b`25lÈKJ<È<C?69^KM(:KdeCc:K:K4KC723l;Dd705B<6 05]f/F~ :KlB`df061;N~ 4K/IC7; 0PB G]f;EC?23Cn:KB<4P4KMN;C7med7A ¯)dy6FC7:<6FDNDkCf;gd7]DNC7:K C747de46 :GMW2B`;E23;N6Fd725l:<d74nDEMN: 6d7;~ 7DE?/16n:KMN6FC$;N4GDE;E616;M ]f~ B`:K0 4 ~ ~C70t]]f C7C*47MN6C7d7MN/1dyG:<C7DN6F;4 ]f~ 6[6kM?MN/1:<GC7C76K61mf4 OÛ0P~ 6[61M MW;47BG:`; B`zel l)6F6F4G; ;,]f23B,Æ ze~ 230596m`]ük 25D ]7~6F64G;Ndy23i?:<6F254KD;056161MWM; ]7op2:K¬4?/F]7DEB`6F4l~ 61614KM; ]7B`0GB<]74?B`MU4?036M C7254G4 ;N6F~ D :< 4G2361;N476Fgt47;N616{4K;]f056{:<D DEM6 ~]f?66F0µD ~67gt6;EDEB]f~6{;N25l:<4:`;E]f2o61MMMWopDE/[/1KGC?C76F614G4G;N;E256FM10|m`M9APd761C7M2|B<MECfK;NC?616{C7D 036[MM4?]76B`d7;NDN61:KMdeB<:GMEMNMWB<: 4G~ ;23/147612fM9250 B`3C?C7MWg ;ND 23B ;N;E6F23l:K4 M ;E47DE2B ]f /1B`lC7gB`m D ~ 76kB<03JK:<DE2;E7l25GC76@]?B`4?M(0361C7D Md7C?z7032 ~ B`;N25:<4?M1=t2306[MR;]f2Æ ~ 23056\]76\MN6\MEB ;E25MWoB`25DE6@]f6 ~ 61M ³9% Xãc´ n&* Ê³&´ n ;E~ 23:<614 05Mk¾~ 6F?:<dfC?:K; C?DM,MFdeB<=yMEB`47MW05:K:325C?~6F23DMk/[M9B0561 pM:<23;N4?0|6FB Mln~ ;NC?=y:<472C7;E61;6FMl]]fMN 6[B`6Mzy;1= :<B`D d7]IS d7DEMNSÛ::<MW/[~C7K7eC?61B`M6F234;N6F/~ gt6\C72|MW4?6F;E;@6B`4GMW]fC?;E/F61d7i?Mde47:K]f23;NDW6n25;@:<DN?4 6 :<~ ~C?70|M B`6FD25DN~ 67866F25:`;\]f;@4?6n6F:<;kl4B`:<B<0;Nm5l*23=yoz7Mb`ÈK25JMWÈ`/[7_tG6XC7m7]f6FAP4f616MS d?~b7Ý9B<m3Y¼DWC7X;EmtD2 ~ ¾]fC7:<6 0523C761~ D D16=7;(~ ]f6FB<0|6*DWB*;E05247B~ :K03l6@C?MU61/MW;Ed7;(7DE:f]:<]fdy 6F6:K4MN]f:<d76 4?DE:<M~ dy:<;Nl:KDE:<MNdf6F2|M;EDB<B`d7J<050569J<C?:<MNB<DE23]76123;NC7:<7D dflM;E/Fl616{M125=tMN ~B<61:<MMEMWl6F: 4l~ 25Ý9/169M C 234G~ ?;EDEDNB6:f~ de]fC7:GC74MN23;@MN¯*23z?]7C?03B<6[474?M69M6F]f05469/i?opd?:K4?B`4 2D ;E~ B`23;E:KJK23:K4DE4PB<d7d7=<DE617/4 6S ~]f2569MN6l]f:<C%;N23oMWM,C?d7MW/[deG:KC7DW6F;[4G=e;Ndy256F6F0|DEMUl?6:K;NC?;EB`MF4Gm ;B`254?MW2;NDE:<2|M,4?2 61B`C7gc]76 opC?®F®F23i ~ B ;N25:<4 03:KDEMk]f6*0|B{DE6 ~ ?6FD ~ 76 çNè í7ë öø÷kókùRï \î fï ö kî fï ö òGï ô ô òGë ó,ï õ ï ;E~ 23:<61DE05DNM A 6[61MW~ dyMn0|B<:<ME474?MW:<2|]?G;NB`25C7:<4G614?;M1Mcm 47T,]:`;E4 23/ ;N6Fl ÿ v 6;B ] ýy 623u ;N~ 6Fl61MWMN;*C76;04 BKMNMN23:<;NMN614G: lÚ;n~ 2|B DN6F;E6[;23]f:K/4%i?4?]C7234}6[C7Mn4wMW:Kd?23C?;NB`61DcMWlàS61D 4?B`6FMWd7;61dyl*]:<z7DNC7;c054w6nB`?MNCf:<:Kg C?CPMWmlS61¾:<4?B`;NMN23D{6FoMIl*6Fgfz?MW/[6F036GlC7?d76F:K054f6<C S = C7]4? 23;N66Flop:KM4 ~?;E:<23:KC?4ÃM1mG]Pük 4B<d747d?:<B`;N61DN6 MW;N;@614?C7B`44 ~ 2;E6<6FmC?l¦T,44?23;N:<61Cclÿ : MWvw6F;s ?ÿ :<C = ýyu /;E6161B<MWMW;4G;@;B<C7C7034:K4DEMMN6F:<4?]fC?MN/FMW6Fi?Sl6F474?z72 MN036,6F~ l:K]Plz7 23;N03l6\61l6?:KMC7C4Ã6; ]f6F/F4?i?MNC?476F42 lde6Fz7B`4f056DS MN6Flz703661MW]7;,6C7MW4I:KC?23MW;NS6F61l4?MNMW661;,l*ez7:<0561CPMeme?:K4fC?i?MP4PBK=yMNMNC7: 47~ 6 25/1M1SmX¾SB<MNDP/1G6C7gf61614l~ d?6 036K=< = >\ DN61J<DE:<C7deB`4G;B`C*;N6[:<MR;E;kB`]70 /i?2347;N61256l~ M :<el:<lC?M16 m C¾74?B`6UD6FMN/1gtG61C7l61d74 03~ 6K6 = 05~ B\:KlMN/1dyG:KC7MN6F/F4 6U~ 6]f6 23;N61lMW6F;EM?:<CeM DE6FJKDN¿@:K:<C7C?deM6Cf^;E223;E052|6FMWl61DNM:K4??M9:KC?]7MB`B`4eCcM05MNBc6F254MNC7]723;N6*6b*]f623;N61~ l6F;*MW6FB`;EDNM1;Nm72 ~ OÛ050P6MF03B`6[JKM92;,47:`]; B C7;E4723:K6 4?MS MWSC7MN2 /1GB`C74G61;N4 6[M~ 6@Ä ?:<C7DE6K6Fd7m DE/1MN6F4G;E6 00 61614?4?MNMN6F6Fl*l*z?z?030366]f]f616[MM\~B`05;W23;E61DN4G25;Ez7M,Cf; 6FMk; 6F; 6[MR;@0|0B 6F4? B`MN6F056FlC?z7D036]76]f610M@B ;W;N;ED DNB`254ez7MNCfB ; ~ ;N25:<dy4e:<M,C7D] 0|C7B{4 ;EDE~ B<052 4?6F4GMNB ; ~ ;E23m :K4 DE6Fmd?.(DN/[?MWB<61G4KC7;E66 ¾B`C7;W:<;N47C?DE6 25Dz7~23Cf05B<3; CeMN6 MR;E6[DNMR612|;,]fDU6d?0561B<25M4?DW;E]f]722|;E2K¬23:KC?/F47DE6{6F474GK/;NC?6F6[64cM03]f6MN:</ied7C?DE47MW:fS26F;E]f234?C7:KMN4?236F;M1l=f4Pz747 Bn03:<6[C?Md?MB<eC7M:<;NC?/F25M1;N032|m/$MW:KB 4?~ MU7056B;E/[z?XBKmPMW¿@69:<]C? MB ~ ~ e:<B 4e;EMWM2|]f]f/F/ DE~ :<DE4e2;EMk6\05i?6{J<]fC761DEJ<6DE/Y 470|lB:K25C?l47M\23: lB<°KB<]f6F047:K4?df;N6<\:Km È?4?mM,_GaDE616MNde;@6 056~ ;EMN2 C76Fd7ldy6F:<4GDN;@; l234?23l6;B`0 mA :<dy/FD B ;E6FC7D\m7]¾ B`:KJ<C7DED@/FJG0561B Mk;E23:<:Kdy4 /FD B ;E~ 6F:KC7DND DEM 61MNdy:<64?; ]c¯ = \] B`B`4?d?M\d?B`C7DN4 ;N61d74?DEB`6F4 l~ 6<2361mD,.(;E?6FlBKKd?C?M16n=y25B`0;WMF;EDNB`25z7JK2Cf;;{]f6[6 MR;$~ :<]f4 :K 4 6F~ DN;Nd?25D,B`05DNB;N23;Nz?25BK:<MW4?647/n]f616FM\4GC?MW:KB`C?4GMR;NS236F;N/[4eM@MW6161l*4z7z?0561BKMMW6?]f:KC?6M]f6FMW61JK03DN:K/[4 M 5R. 5S. U. V. -T. 9S. -T. XW. V. ZY. gk. \[. Q. ]. _^. a` b4 >. dc e4. f4fc. g k. [. g8. ih. . [x, a]. [bonbons, beaucoup]. x. . (X, A). kj. a beaucoup . . A ([bonbons, beaucoup][soda, gk S =< s1 · · · sg > g s = (X, A) k < ([bonbons, beaucoup][jeuxvideos, peu])([soda, beaucoup]) > 23 C Tc c I t[i] i t. peu]). X. l. Pm. i. ω. m. min. RNTI-E-3. minSupp = 0.55 max. 510. >.

(13). ⊥.

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(15) n±. . . X F Supp(X,A) =. S(c, (X, A)). i. c∈C. |C|. 511. RNTI-E-3.

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(17) 506[]76FMR61l; M61~;E4KDEB`B<;k0 ~ 4?DNC7ME6[05B MW/ ~dy;E~ 6 23:K:K~ l;N4?6FM1lD@m`0µ¿,6 :</10D B< B<]f47J<DEl6DE/F:<]7JK2561B`4?M;NM125=<23:<;N¯94I61ld?]fB<MN6[DW6M9;E; 23MMWDC??]fd7:K6@deC?:K05MB9DW; DE]fM96/1;Nl]f614t61B`MC?D MF~23;Nm761.(6l6d7MW~ DE6F2 :<;E23dyMl:K]fdyMN6/F:K6MN0|Bn6]7B`C7MW4e/[4nKM@C?d?86FB`4D 25:`~~ :K;6<C7m6FD ;(OÛM0B`6o0B`gfm5=KC7?b`;B`ÈKCe/FÈ`MRJK_G;EB`2So = 4?4?:<:`;NC?25M@:<4Id7DN]7:K6 de:G~ 7MW:K6F4?lM254PC7me476*T@4l2|~ MN7661l6F4c254 Ý9~ C :K DNDEDE6961MN6dyÆ :<4?~ B ]~ 6¯]C747C76*4c234?;E6FMW0;EB<d?4 B`~ D 2|~ B :K;EC723:KDE4cMdedeB`:GD,MNMN025 z7254G036;N61]7DNl61M,/123]7;N2561B<l23DEMW66F;E]fM\6]f0|B6 0|2547B$23;NMN25/1/1GM@C7de614:KC7~ 6D,C7~ B<4 4?~]f032|25]76FB 4G;E;,66]7;kB<2304?M@MF B`0561JKM@2;,;ND ]fB`6 4e~MNB:<~4?;NMN256F:<D 4e M,61D ]fC~ 6F05~ C703252 6F4G]7;[6myd7¾05C?03C?MMNop256F:<C7DN;@D M ]f~61?J<6FDE/<l=?23M14e M@250Pdy6[6FMR;C ~ 6F:<4Gl;kd7ÀF05;N6DE;[6 = dy:<C?D,036 ~ B`0 ~ C70P]fCcMNC7d7dy:<DN;1m x x µus ý lSRB<º D L~ :<7C`6«RB<:<]7C7:<D M@df;E¯/F6\deB`d?DNB`;ND 25Dk¥@]f6[§?M¨[©?;ND ª¼B`ªÛe4eMNB ?~ 1;N F25:<4edyM@:<]f=GC?CB D ~~6 03B`~ 256F0 C?~ 4GC?4$;*0361MWYKDU61=?C705ie69250J<MWC7C?DEd76*¯de^7È7:K=em DWbf;47mK:<]fT@Ce64 Mk0|BB<~ 703MN561:</1l4?GC7M,234{61234056[3~CeMR6 ;UMR;E~C7DNB<6144?D@;E]f0|DNB$2|25]7d7]fB 056;E/F6;S de~ :<B`4GDN;N;NG6F614eC74?2B`B`44G~ :<;,~ 4G60|;NB]7256F61MW4GM/[; G]fC723¬6F4/FDE~ 6F64G]f;EM/R«W23¯;N61;ElDN:KMWC6F;E M1/1m`6<¾=f:<0C723;ND61K25l¦C?472 23;N~MN25C7:<6FDE2D DN05B`6[6MW4Gdyd7;,:<DEDN:4?6 ~]9~ 617¯@ME6FMWD05CeBk~ MF7MW= /9/[2507GB`C7°254?6FB 4MN2 ~~ 6(DNG/[C7]fB 69/W;N«W2505¯:<614M,;EDN]]f:K61C C7J< 4 DE/1/16@~ M7 ]61l B`d725X4 S = 0]P 2Y<;E= 6Fl DN6 ~ 76FD ~ 7/k =?]f:K4 ~ 0366 ;~ 057661]7l6FJ<234 DE/] B`d76[d?MR;,B<DWl;E6F2|4?MB<¯k4 «R~ :<6C7Dd?B<D m<¾:<C7D0|Bk;ND B`4?MEB ~ ;N25:<4 4?MWC?2;E6<=[de:KC7DP0|BU~ ;NB<D mDB`4?]eMEb B ~ ~ ;N:<25:<4G4;E23]?614Kbf;9=C?04\23;N4?61l:<C 61B`C ~ 761l23461MW; G~ C7DE2/F/61MW;056d7DE6Fl256FD2;E6FlV]f605BnMN/S ~4?G:<C7/F4G6<61;Nmf4 25~6F64G035;6 ~ B`;N~ :K4?:KC?]74KM25;E]7236105B`614G;NM;6Km/F05/Flm DN6F6 4G61~ ; MWyM;{.(]fl:<6nC?25MD105B"=G¯036 MN«R/1:K~ G7C7C761D 6Fl4 ~ 25B<~ 4 6D]?SRb ºm~61:KMWA ;,4KB;E]f2361;N:<D 4G4 B`; ~ 4elMNB :f~ ;N]f2523:<i?4Ã/6F]74 ^ m 61MW;61614?MWMN; C72~ ;E056n:KM 6g7~ B`B`lD2323S0 ~]P:< B<4?d7MNd?6FD B` DN6K;N61=?4?dyB`:<4 C7~ D6<]fme61>,Cf25g4?MW~27=?=6F056 l~ 6 ~ 2574?~ 61Mk7l61B<l23CI4 25l4cÀF61lMW; 616~MWMW03;@:G;E/FBKMF05my]f2 l¿,6/125]747B<6/*47d?l]7B<6:<D 25~054?B{:<M1C7=7032|D 03MRM16;E=?6*d?G]fB`C76[D 6 ~M :K~ ~ 6FC7705D C761Ml261]725MW4?6;@M:<ldydf6F:<;E2523C?0 l3D@612|C705MW6D\/*~]76056F;k2361J<4?4GDE6/; Y~ :<~lB`lD69B¼°K23B`4e4G]f;\25GC7C74%/]7ie6FJ<J<C7DEDE/6k]P_em B<d7d?B`DN;N614?B`4 ~ 6*254fop/1DN256FC7D9¯ mAP6d?B`D ~ :KC7D M@MN6dy:<C7D MNC72;6F4eMWC723;N6 ¿ +À > Á. g. Ãm. ÂD> $?

(18) . < ([bonbons, peu])([soda, bcp]) >. ω. (∅, ([bonbons, peu]), 0) rechCour rechCour = d1[1] ch1 ([soda, bcp]), 0.75) ch1. seq degCour (< ([bonbons, peu]) >,. ch2 ← (< ([bonbons, peu]) >,. ([soda, bcp]), 1). [bonbons, peu]. [soda, bcp] ch1. ch1. g ch2. ch2 ([soda, bcp]) >, ∅, 0.75). (< ([bonbons, peu]). ch1. ch2. _ tÌ ,Ñ 3Ì KÌ,Ñ7Í NÏ Ð Î (Ñ7Ð`Î 3ÌÏ Ì. L F\Ä¾Å ? "( F=. M. 513. MK%. M,(. ?(@' ?AB!«ª. RNTI-E-3.

(19) x x ÿ s ý ý su s[r ÿ s ~6[:<MR;,C7D A;EMDN :KB<:<C03D JK ]f:</K:KDE=f472;EC74774 /l~]f6 76[61M,¥,l;E§eDE254n¨1B<©?4?61ª¼MNMWBªR; e~ ;E~23DE:K7/F4? [/9 MB{] C76 C7~;N42503032|6MW~ 6k05MW2 C76F05B4Gd?;1deopmy:<:KAP4 DW;@~:<;ND ]f25ME:<69K4 C?0692;E036F6ld?MWDN6F61;1lmyAP256F61DkM2;N;ED 6FB`l4?GMNME6C7B ;\~2y;N]7DN25/[6:<B`4?0505MB$2 MNMN6,MWC7/[C72K4C?B<6Fd?4G4 ;NB`~61DN6MS ¿ +À Æ. Ç. ÉÈ. . $>. F indT otallySeq. ÊgË)Ì"ÍBÎÏ Ð}Ñ Ò)Ò ÓZÔ Õ§Ö×ÙØbÚÛÜkÝ5Þ ñ ÜÛÜkÝ¾Þ g ß2àZµ g á k á³}âbã$äå7¶æ7å¾æ7çK¶nè´ èç§é}å-µ_êµnåb¶n³åbë¹ìní å¾ènåéîçK¶n³<çKæeé´ ·-¶n³ï¹ðnçKîæb·-änî>´ î m µní åènåbò-îâ³}äðnð ·-î>éènå¾í@ç9ë«åb´ í í åbänî>åî>å7ðîâb³}åb¶Dé<ç§é´ ·-¶Eènå g á>ó ´ ¶n³é}çK¶næb´ âbå5ðçKîë«´kí åb³_éîçK¶n³<çKæeé´ ·-¶n³ènå¾ô ÝPùúùEÛû üKý-þkÜü ù üPùýþ Üüúù 9þkÜü ø → ÿ>ø Chemins õö2÷.ø "$&%(')&*+,-(.*+(/ 0*1 2 345768 79 3:,-$;<"$;

(20) !#"$ ß g ß2à g ß2à>=

(21) +"$?;0$*87 ) 3: &8"$ @"$?*A7 @"B2 C$C*57!!"7 @"3 DE7*+;& F345768 7& G"$8 . Chemins ← HInåbë«´ ¶BJ ∅ µ g óLK Mî>³é7µ!N$O. =. û üPù. PþkÜü. û ü§ù PþkæIÜçKü ã?änå¾é}îçK¶n³}çKæbé´ ·-¶ t ∈ ôRQ ÷ T æIçKã?änåðçKî>æ7·-äî³ ch þZü ∈ Chemins µ$¶n·-¶ ë«´ ³_ïES·-änîgï¹í@ç5é}îçK¶n³}çKæbé´ ·-¶ t Q ÷ ÷EJ T ch ¶n·-¶ æbí ·-³OVUö ø þkü t O< U ÷EJ

(22) chK î>åb;æ&I!3:H";·-änî 2 34∈ 561 9ö 3Wø "$?$*+"$/7X834576Y"$8+2 34561 9 -C*3:*1Z 734. f. t ch K ènåbòH"·-änî ← ch K ènåbòHf·-äî1[ >[x,a]∈ch \ ]&^+_5àLbc>] αa (t[x]) d e T ð èç§é}åJ ch O d. f Ú ÷ Ú T÷ û ü§ù P÷þkÜü ÷ úùhg8i ájk

(23) S l*+/*+(/ch K î3:åb3æI!H"!·-8änî_68 Q 3:*+÷ $m3mnC 3mo7 "h(/613:l*A; = T þZü ÷EJ+J g óLK ò-åeé7J SO ∈ t OVpqJ >[x,a]∈gS.get(j)αa (t[x]) > ch K ènåbòH"·-änî7r Ss:O+OUiö ø ¶Pgå(þktEÜu_ü åbæI!úH"ù ·-änî i ← g ó!û K ò-åbüPé7ù J SO d ´ j >S ájFQ ÷ ¶nåtó$åbã ← ¶nåtó?å7ãv[ g ó!K ò-åbé7J+´4O d ¶nåþ tEÜwü åbòHf·-äî ← ¶å(tEwåbòH"·-änî8[ ch K ènåbòH"·-änî7r ´ s$d f ÚxPg. ÷ ¶å(tEwåbòH"·-änî. ← ¶nåtEwåbòHf·-äî8[ >[x,a]∈gS.get(j) αa (t[x]) d ä ð èç§éåJAJ+¶nåtó$åbãZµk¶nåtEugåbæI!H"·-änîbµZ¶nåtEwåbòHf·-äîO+OBd ← Chemins∪ n T f Ú Chemins Ú P÷ þkÜü ÷ y. f ÚyP÷ þkÜü T ÷ þkü óLK !Mî>³é ,-∈} J2¶3:·-l ¶BJ&|B Vîåb*ë«+´ 8 åbîA |B39çK³} ³<çK*+ò-å!O+OAOk ø C!*A7683:*@34561 V"$~ ! ÷zJ+

(24) 5J gh t Oz(/p{ 61 ;U&*+ö 8 k f. ch ← HInåbë«´ ¶BJ ∅ µ g óLK Mî>³é7µ >[x,a]∈gS.f irst αa (t[x]) OLd Chemins ← Chemins ∪ ch d. e. Ú T ð èç§éåJ2æI!OBd ÷ ÷

(25) 3:613:!&3:}"$ G634; 1o; @(/613:; HInåbë«´ ¶n³K ðé´ ë«´båJ5OXd = f ÚyPþkÜü ÷ û ü§ù PþkÜü T æ IçKã?änå5ðçKî>æ7·-äî³ ch þZü ∈ Chemins Q ÷ ÷ J ch ¶·-¶ æbí ·-

(26) +³7OV 34U z 68ö34!$ø m3ml"$ @(/76834; G39!8$,-*+;C @55~ ! H"äé7J OLd = f Ú T ch f y Ú P÷ þkÜü ÷ ÷

(27) !8$;m3m7;C! ~7X1 8673:4 7*VC*A$* 8$6EC! f. ch ← Chemins.f irst d m ←

(28) (ch K ènåbòH"·-änî ) d. «ù?ÝPþkÜü-Ú ùü. md. Chemins.

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