scieee AI-readable full text Open interactive document viewer

Fuzzy Grammatical Inference Using Neural Network

Blanco Morón, Armando,Delgado, A.,Pegalajar Jiménez, Mª Carmen

Abstract

We have shown a model of fuzzy neural network that is able to infer the relations associated to the transitions of a fuzzy automaton from a fuzzy examples set. Neural network is trainned by a backpropagation of error based in a smooth derivative [Blanco96]. Once network has been trainned the fuzzy relations associated to the transitions of the automaton are found encoded in the weights.

Full text

sYbs m 7BP ]B8}Z$t x w dM D dnnTd;( 3Z99k ps88s${sj ytPt{ ZR$t WZsj WbB, V jst{B V *jsIB stI ] _sjs`s *}B I ]$t{$sR I js ]B8}Zs{$?Bt  ytj$t{$s V$h{$sj eq7y ytPB8?s${s =t$%R$IsI I pstsIs V% I VtIsjZ{?s nM dM(d pstsIs w 7}s$t D T8s$jU 8{s8toI{Rs$ZR VARs{ G Ys% RYBbt s 8BIj BP PZ99k tZsj tbB, Ys $R sAj B $tP Y js$BtR sRRB{$sI B Y stR$$BtR BP s PZ99k sZB8sBt PB8 s PZ99k -s8}jR R WZsj tbB, $R s$ttI Ak s As{,}B}ss$Bt BP B AsRI $t s R8BBY I$%s$% > d H  !t{ tbB, YsR At s$ttI Y PZ99k js$BtR sRRB{$sI B Y stR$$BtR BP Y sZB8sBt s PBZtI t{BII $t Y b$YR kbBIRU 3Z99k VZB8ss 3Z99k i{Zt WZsj WbB, 3Z99k ps88s${sj ytPt{ d ytBIZ{$Bt dd ps88sR ps88s${sj ytPt{ stI i{Zt WZT sj WbB,R yt Y jsR ksR s88s${sj $tPt{ ZR$t {Zt tZsj tbB, YsR At s b$Ijk IsjI b$Y }BAj8 yt }s${Zjs $ YsR At RYBbI Ys {Zt tZsj tbB, w iWW D s {s}sAj BP $tP$t Zjs s88sR >1 ; x d(H *Z$t Y s$tt$t Y {Zt tbB, }s$$BtR $R R}s{ BP RsR $t bjj IhtI $BtR Ys }Rt Y {BR}BtIt RsR BP I8$t$R${ ht sZB8sBt w *3V D bY${Y $R $I B jst <Bb% PZ99k s88s${sj $tPt{ ZR$t tZsj tbB, $R st B}t }BAj8 k yt Y$R }s} b }Rt s 8BIj BP PZ99k {Zt tZsj tbB, Ak 8stR BP bY${Y $ {st A $tPI PB8 RJZt{R b$Y 88ARY$} IR B RsR BP sZB8sBt Y PZ99k s88s sRRB{$sI qY R{Y8 BP Y$R bB, $R Y PBjjBb$tU hRjk $ b$jj A IR{$AI Y s{Y${Z BP Y }B}BRI PZ99k tZsj tbB, t- b b$jj R Y s$tt$t }B{IZ stI YBb sZB8sBt $R -s{I 3$tsjjk BAs$tI RZjR PB8 Y R$8Zjs$Bt BP s R}{$h{ -s8}j b$jj A }B%$II dnn dn; V jst{B V *jsIB m ] _sjs`s d1 3Z99k ps88sR stI 3Z99k ps88s${sj ytPt{ 3Z99k iZjs ps88s H $R s JZsIZ}j H ) c],x, h,C k bY ] stI x s RR BP tBtT8$tsj stI 8$tsj Rk8ABjR R}{$%jk  h $R s R BP }BIZ{$BtR $t Y PB8 \   y B \   y4 bY \,4 ; ]  y ; x stI  ; >( , dH k C $R Y Rk8ABj bY${Y tsR Y s88s yt s PZ99k s88s r  Y RJZt{R AjBt B Y jstZs tsI Ak Y s88s b$Y s I BP 88ARY$} qY I BP 88ARY$} t w ? D BP s RJZt{ ? ; x   $R Y 8s-$8Z8 %sjZ BP sjj Y %sjZR BP Y }BRR$Aj I$%s$BtR BP ?  bY Y %sjZ BP s R}{$h{ I$%s$Bt BP ? $R Y 8$t$8Z8 I BP 88ARY$} BP Y }BIZ{$Bt ZRIU t w ? D ) t  ) F ? ) 8s8$t C  F ? > t w C   d D , t w  d   1 D ,333, t w  E  ? D H Vt sZB8sBt $R ts8I PZ99k bYt Y$ RsR s {Yss{$9I Ak PZ99k RR stI Y }BIZ{$BtR BP stRbR stI PBjjBb$t RsR s Ps{$j$sI Ak Y s}}B}$sI PZ99k js$BtR V PZ99k sZB8sBt Z  $R s PZ99k js$Btsj RkR8 IhtI Ak s JZ$tZ}j Z ) c  , S , ' , o , w k bY  $R s tB 8}k ht$ R BP $t}Z RsR w $t}Z sj}YsA D  S $R s tB 8}k ht$ R BP BZ}Z RsR w BZ}Z sj}YsA D  ' $R s ht$ R $ttsj RsR o $R Y PZ99k js$Bt $t 'S stI w $R s PZ99k js$Bt $t ''  p$%t s PZ99k s88s r  -$RR s PZ99k sZB8sBt Z Ys {Bt$9R Y Rs8 jstZs bY${Y tsR Y s88s r  Ys $R U w r D ) U w Z D 3 3Z99k s88s${sj $tPt{ >nH $R IhtI sR Y }BAj8 BP $tP$t Y PZ99k s88s${sj ZjR B PZ99k }BIZ{$BtR Ys {Yss{$9 s PZ99k s88s PB8 s R BP PZ99k -s8}jR BP s$tt$t *Z B Y js$Bt Abt PZ99k s88s stI PZ99k sZB8sBt Y }BAj8 BP PZ99k s88s${sj $tPt{ {st A PB{ZRI sR Y BAt$Bt BP s PZ99k sZB8sBt Ys {Bt$9R Y R BP jst$t -s8}jR stI PB8 bY${Y b BAs$t Y R BP }BIZ{$BtR AjBt$t B Y s88s bY${Y tsR RZ{Y -s8}jR !Z }BAj8 b$jj A {tI $t BAs$tt$t Y PZ99k stR$$BtR sRRB{$sI B Y PZ99k sZB8sBt w PZ99k js$BtR Ys Iht Y sZB8sBt "8B%8t" D PB8 {BZ}jR BP -s8}jR w   # D bY  $R s RJZt{ BP {Yss{R B }B{RR Ak sZT B8sBt stI # $R s PZ99k R bY${Y }RtR Y 88ARY$} BP s{Y RsR BP sZB8sBt Bt{ $t}Z R$t $R sI 3Z99k ps88s${sj ytPt{ ZR$t WZsj WbB, dnx 1 qY 3Z99k i{Zt WZsj WbB, ......... ......... ......... ....... ...... 0 0 W II SSS t+1 t+1 t+1 0 1 .......... SS S 01 tt t tt 0 L-1 N-1 N-1 min min min min min max maxmax min S 1 S N-1 S mmm Hidden Layer Recurrent Neurons Input Neurons Output of Neurons 3$Z dU s-T$t WZsj WbB, qY tbB, b }B}BR 3$Z d {BtR$RR BP ] PZ99k {Zt tZBtR jsAjjI ? i  U $t}Z tZBtR tBT{Zt { > stI ] 1  U b$YR jsAjI P 7i>  qY$R tbB, s{{}R st $t}Z RJZt{ BII $t $8 stI $R Ikts8${ $R }PB8I $t Y PBjjBb$t bskU ? 0 Ld 7 ) 8si,> 8$t w P 7i> ,C 0 i ,{ 0 > D w d D es{Y Rk8ABj BP Y $t}Z RJZt{ $R t{BII $t $t}Z tZBtR $t s{Y R} BP $8 0 sR PBjjBbRU y D yP $t}Z {Yss{ $R ( Yt { ( ) d stI { d )( K D yP $t}Z {Yss{ $R d Yt { ( ) ( stI { d )d eJZs$Bt d $R %sjZsI $t s{Y PZ99k tZBt ? 7 B {B8}Z Y %sjZ BP PBjjBb$t Rs $t $8 0 Ld 7s$t %sjZ APB stk $t}Z bsR Rt $R C ( ( )dstI C ( i ) ( PB sjj i W )( dnE V jst{B V *jsIB m ] _  sjs`s 1d qs$tt$t }B{IZ qY Bsj BP s$tt$t Y tbB, $R B h Y b$YR $t BI B Y R BP $t}Z -s8}jR }BIZ{ Y R BP b$RYI BZ}ZR qY B PB s{Y PZ99k tZBt $R {B8}ZI Ak 8$t$8$9$t Y RJZs BP Y I$&t{ Abt Y b$RYI BZ}Z x 7  stI Y BAs$tI BZ}Z Ak tbB, ? W 7 PB s{Y }stR ZRI $t Y jst$t ? W 7 b$jj A Yt{ Y %sjZ BP s{Y tZBt Bt{ Y }Rts$Bt BP st -s8}j RJZt{ YsR ht$RYI G b$jj {B8}Z Y B Ak ZR$t Y PBjjBb$t -}RR$BtU o 7 )d 1 w x 7 ? W 7 D 1 w 1 D bY ? W 7 )8si,> 8$t w P 7i> ,C W  d i ,{ W  d > D w n D A$t x 7 Y I BP 88ARY$} B Rs 7 BP sZB8sBt Z stI ? W 7 Y I BP 88ARY$} B Rs i Ys tbB, $%R sR RZj  qB h b$YR b ZR s s$tt$t sjB$Y8 Ys Z}IsR Y b$YR s Y tI BP Y }Rts$Bt BP s{Y -s8}jR RJZt{ G b$jj Z}Is Y b$YR $P B $R s Yst   Ys $ b$jj A {YBRt I}tI$t Bt Y s{{Zs{k Ys $R b$RYI $t Y RZjR 7B Z}IsI ZjR BP Y b$YR b$jj A n P 7qE )  (o 7 (P 7qE )  w x 7  C W 7 D 3( ? W 7 (P 7qE w ; D ( ? W 7 (P 7Ez ) ( 8si,> 8$t w P 7i> , ? W  d i ,{ W  d > D ( 8$t w P 7Ez , ? W  d E ,{ W  d z D 3( 8$t w P 7Ez , ? W  d E ,{ W  d z D (P 7Ez w x D N A h dU ( 8s-8$t i,> w P 7i> , ? W  d i ,{ W  d > D ( 8$t w P 7Ez , ? W  d E ,{ W  d z D ) w E D ( 8si 9 ) E> 9 ) z >8$t w P 7Ez , ? W  d E ,{ W  d z D , 8$t w P 7i> ,C W  d i ,{ W  d > D H 8$t w P 7Ez , ? W  d E ,{ W  d z D stI _1U h 1) ( 8$t w P 7Ez , ? W  d E ,{ W  d z D (P 7Ez w  D qY I$%s$% BP PZt{$BtR E7z w r, D stI Ey? w r, D  -$RR PB rc stI rk  AZ $ $R tB IhtI $t r )  ( 8$t w r, D (r ) F d$P rc ($P rk k  ( 8sw r, D (r ) F d$P rk ($P rc k w M D 3Z99k ps88s${sj ytPt{ ZR$t WZsj WbB, dn VR $ $R ZRZsj >H b b$jj sRR$t $t stk {sR PB r )  Y %sjZ B Y $Y B Y jP BP Y {BR}BtIt I$%s$% ( 8$t w r, D (r ) F d$P r   ($P rk k  ( 8sw r, D (r ) F d$P r   ($P rc k w  D <Bb% b Ys% {YstI Y$R "{$R}" AYs%$BZ Ak s "PZ99k" Bt bY${Y $R {s}sAj B {s}Z Y sj 8t$t BP w r   D B w r   D $t st $8}{$R {Bt- G b$jj ZR sR s 8sRZ BP Y I BP $t{jZR$Bt BP } $t k Y p[BIj:R $8}j${s$Bt 7B $ 8s$tR U ( 8$t w r, D (r ) F d$P r   r $P rk k  ( 8sw r, D (r ) F d$P r    $P rc k w d( D k s,$t $tB s{{BZt }%$BZR JZs$BtR b BAs$t Y PBjjBb$t RZjRU h d) F d R$ 8$t w P 7Ez , ? W  @ E ,{ W  @ z D  -\ 8$t w P 7Ez , ? W  @ E ,{ W  @ z D R$ 8$t w P 7Ez , ? W  @ E ,{ W  @ z D c-\ k w dd D h 1) T z Z dR$ P 7Ez \ C W  @ E ,{ W  @ z i C W  @ E R$ C W  @ E \ P 7Ez ,{ W  @ E z { W  @ z R$ { W  @ z \ P 7Ez ,C W  @ E i [  ` w d1 D k {B8A$t$t Y %sjZR BP h d stI h 1U (C W 7 (P 7Ez ) T                   z                   Z $P -{] ) P 7Ez T z Z P 7Ez  -\  p d)d P 7Ez c-\  p 1) P 7Ez $P -{] ) C W  @ E T z Z C W  @ E  -\  p n) C W  @ E C W  @ E c-\  p ;)) C W  @ E  C W  @ E $P -{] ) { W  @ z T z Z { W  @ z  -\  p x) { W  @ z { W  @ z c-\  p E) { W  @ z  { W  @ z bY -\ ) 8si 9  E,> 9  z >8$t w P 7i> ,C W  @ i ,{ W  @ > D H -{] )8$t w P 7Ez , ? W  @ E ,{ W  @ z D !t{ Y$R $t{8t $R {sj{ZjsI b ZR s 8B8tZ8 8 s,$t $tB s{{BZt $t Y {sj{Zjs$Bt BP {Zt $t{8t Y $t8I$sjk }%$BZR $t{8tU dnM V jst{B V *jsIB m ] _  sjs `s n P 7i> ) 3 n P LqQ 7i> L w d  D 3 n P 7i> w dn D =RZsjjk b Ys% s,t )( 3 x 3 11 7YBb$t BP qs$tt$t e-s8}jR yt$$sjjk b$YR s s8IB8jk {YBRt $t $t%sj >(dH qY s$tt$t Iss sR }%$BZRjk PI {BtR$R BP }s$R w ,# D  bY  $R st $t}Z RJZt{ ? @ ?  333? q  ? 7 ;\ ( , d i k # ) w @ w ? D ,  w ? D ,333, ] w ? D D  A$t ] Y tZ8A BP sZB8sBt RsR stI Y tZ8A BP PZ99k tZBtR BP Y tZsj tbB, 7s$t %sjZ PB PZ99k tZBtR ?  7 $R 9B -{} PB tZBt ?   Ys $ b$jj A JZsj B d WbB, RsR s$tt$t b$Y Btjk 1( -s8}jRU qY 8s$t$t s$tt$t -s8}jR $R R}ssI $t BY R Ys tbB, b$jj RZIk Bt{ $ YsR jstI Y hR 1( -s8}jR B IBt s R}{$h{ tZ8A BP }BJZR ZtIRstI$t Ak }BJZ Y }$BI Ys tbB, R}tIR $t }B{RR$t Btjk Bt $8 sjj BP RJZt{R BP s$tt$t GYt Y tbB, YsR jstI $R R BP s$tt$t }st B -{II Y 8s-$8Z8 tZ8A BP }BJZR  Yt $ RZI$R Y 8s$t$t R BP -s8}jR Ys $ YsR tB Rt k s{$t $t Y PBjjBb$t bskU $P Bt RJZt{ BP Y$R R $R tB {Bt$9I w ok6 D  Yt $ $R $t{jZII $t Y s$tt$t R stI $t BY {sR }B{RRR stBY Bt qY tZ8A BP RJZt{R B $tBIZ{ $R j$8$I B d( $t BI B s%B$I Y B%R}{$sj$9s$Bt BP Y tbB, y $R 8I {k{j B Y R BP s{$BtR BP }B{RR$t Y RJZt{R BP s$tt$t R stI RZARJZtjk RZIk$t Y R BP RJZt{R Ys $ $R tB Rt stI $t{jZI$t $P $ $R tB {Bt$9I =RZsjjk b ZR 1( {k{jR sR 8s-$8Z8 B s$t Y tbB, bYt% s RJZt{ BP s$tt$t R bsR }B{RRI stI $R B bsR s Yst 6 b b$jj }sRR B h Y b$YR Ak ZR$t }%$BZRjk $%t JZs$BtR 1n e-s{$Bt BP 3Z99k VZB8sBt !t{ tbB, YsR jstI Y s$tt$t -s8}jR Y jstI PZ99k sZB8sBt {st A -s{I Ak RZIk$t Y b$YR BP {Bt{$BtR BP Y PZ99k {Zt tZBtR Ys $R Y b$Y P 7i> }RtR Y I BP 88ARY$} BP Y stR$$Bt BP Rs i B Rs 7 BP sZB8sBt Ys%$t sI Y $t}Z Rk8ABj >  qYPB b {st AZ$jI Y PZ99k js$Bt w >(H k w >dH sR s PZt{$Bt BP $t}Z >  > ;\ ( , d i U w >(H ) C h h H P  P @ 3P ]  P @ P @@ 3P ] @ 3333 P  ]  P @ ]  3P ]]  I n n O w >dH ) C h h H P @ P @@ 3P ] @ P @@ P @@@ 3P ] @@ 3333 P  ] @ P @ ] @ 3P ]] @ I n n O n 7$8Zjs$Bt G Ys% {YBRt sR -s8}j Y sZB8sBt Ys bB,R sR -}RRI Ak Y PBjjBb$t PZ99k js$BtRU 3Z99k ps88s${sj ytPt{ ZR$t WZsj WbB, dn w >(H ) C h h h h H ( 3 M( 3 1( 3 d( 3 1( 3 d ( 3 n( 3 d( 3 ( 3 1( 3 d (( 3 d( 3 1( 3 Mx ( 3 d ( 3 d(( 3 ( 3 1( 3 d ( 3 d( 3 d( 3 1( 3 d( 3  I n n n n O w >dH ) C h h h h H ( 3 d( 3 ( 3 1( 3 d( 3 1 ( 3 M(( 3 d( 3 1( ( 3 1( 3 d(( 3 d( 3  ( 3 d( 3 M( 3 d(( 3 d ( 3 d( 3 d(( 3 1( 3 M I n n n n O VR $ {st A BAR%I $t 8s$-R Y sZB8sBt YsR x RsR A$t htsj RsR Y BtR ( d stI n yt$$sj Rs b$jj A ( stI $ b$jj A }RtI Ak {  ) D d(((( i 3 qY tbB, ZRI B jst Y$R sZB8sBt YsR At s tZsj tbB, b$Y x PZ99k {Zt tZBtR stI bB $t}Z tZBtR qY }ss8R ZRI B jst Ys% At s jst$t s$B  )( 3 1  st stRb$t Bjst{ 6 )( 3 (((x stI 8B8tZ8 8 )( 3 x yt Y$R R$8Zjs$Bt b tII n {k{jR BP x(( }BJZR B BAs$t s jst$t RZjR BP d((0 BP -s8}jR qY BAs$tI RZjR Bt{ tbB, bsR s$ttI b 2  )( ! M((( 2  d )( ! d((( 2 (d( )( ! n((( 2 (dd )( !  2 (1( )( ! ((d 2 (1d )( ! 1((( 2 (n( )( ! 1((1 2 (nd )( ! (d1E 2 (;( )( ! ((( 2 (;d )( ! (n1n 2 d(( )( ! 1((( 2 d(d )( ! ((( 2 dd( )( ! (MM 2 ddd )( ! (dM 2 d1( )( ! (E( 2 d1d )( ! ( 2 dn( )( ! d(M( 2 dnd )( ! MEx 2 d;( )( ! (MME 2 d;d )( ! ( 2 1(( )( ! d((( 2 1(d )( ! 1((( 2 1d( )( ! (d; 2 1dd )( ! (((( 2 11( )( ! 1((( 2 11d )( ! (((( 2 1n( )( ! 1((( 2 1nd )( ! (((d 2 1;( )( ! d;E; 2 1;d )( ! (((( 2 n(( )( ! d1d( 2 n(d )( ! d1E( 2 nd( )( ! dd 2 ndd )( ! dEE 2 n1( )( ! d1d; 2 n1d )( ! 1(1E 2 nn( )( ! 1xdE 2 nnd )( ! 1n; 2 n;( )( ! d1x 2 n;d )( ! dM 2 ;(( )( ! (((( 2 ;(d )( ! d 2 ;d( )( ! (((x 2 ;dd )( ! (((( 2 ;1( )( ! (((( 2 ;1d )( ! M;; 2 ;n( )( ! 1xd1 2 ;nd )( ! (((( 2 ;;( )( ! EM1 2 ;;d )( ! M1Md 7B PB $tRst{ Y 8st$t BP b$Y 2 1nd $R Ys Y sZB8sBt YsR s stR$$Bt b$Y I BP 88ARY$} ((((d PB8 Rs n B Rs 1 sI$t Y $t}Z Rk8ABj d qYPB b {st -s{ Y PZ99k sZB8sBt sRRB{$sI B Y s$tt$t -s8}jR Ak AZ$jI$t Y PZ99k 8s$-R b$Y Y R8st${ BP }%$BZR -s8}jR yt Y$R bsk Y PBjjBb$t PZ99k js$BtR s BAs$tIU M >(H ) C h h h h H ( ! M((( ( ! 1((( ( ! d((( ( ! d1d( ( ! (((( ( ! n((( ( ! (MM ( ! (d; ( ! dd ( ! (((x ( ! ((d ( ! (E( ( ! 1((( ( ! d1d; ( ! (((( ( ! 1((1 ( ! d(M( ( ! 1((( ( ! 1xdE ( ! 1xd1 ( ! ((( ( ! (MME ( ! d;E; ( ! d1x ( ! EM1 I n n n n O M >dH ) C h h h h H ( ! d((( ( ! ((( ( ! 1((( ( ! d1E( ( ! d ( !  ( ! (dM ( ! (((( ( ! dEE ( ! (((( ( ! 1((( ( ! ( ( ! (((( ( ! 1(1E ( ! M;; ( ! (d1E ( ! MEx ( ! (((d ( ! 1n; ( ! (((( ( ! (n1n ( ! ( ( ! (((( ( ! dM ( ! M1Md I n n n n O d;( V jst{B V *jsIB m ] _sjs`s ; ]Bt{jZR$BtR G Ys% }B}BRI s PZ99k {Zt tZsj tbB, bY${Y $R {s}sAj BP $tP$t Y sRRB{$sI sZB8sBt PB8 RJZt{R BP -s8}jR BP RZ{Y PZ99k jstZs G R$8Zjs Y AYs%$BZ BP Y tbB, $t Y jst$t }YsR PB s R}{$h{ -s8}j RYBb$t Ys Y tbB, jstR B $tP Y sZB8sBt sRRB{$sI B Y s$tT $t -s8}jR {B8}Z$t $t Y$ b$YR Y js$BtR bY${Y {Yss{$9$t Y AYs%$BZ BP Y sZB8sBt B jst iPt{R >dH jst{B V *jsIB  iJZts y yIt$h{s$Bt BP PZ99k js$Btsj JZs$BtR Ak PZ99k tZsj tbB,R 3Z99k 7R stI 7kR8R zBjd }1dxT11E w dx D  >1H ]j8stR V 7%stT7{Y$A * stI {]jjjstI F dM 3$t$ Rs sZB8ss stI R$8}j {Zt tbB,R WZsj ]B8}Zs$Bt d w n D  n1TnMd >nH 3Z  7 7kts{${ _st i{Bt$$Bt stI V}}j${s$BtR _t${ <sjj etjbBBI ]j$&R WF w dM1 D  >;H p$jR ]N stI !8j$8 ]G d1 ytR$t ZjR $tB {Zt tZsj tT bB, _B{ d1 yeee GB,RYB} WZsj WbB,R 7$tsj _B{RR }} dnT11 ]B}tYst *t8s, >xH p$jR ]N $jj ]  ]Yt *]Yt << 7Zt p stI N O] d1 Nst$t stI -s{$t ht$ Rs sZB8ss b$Y R{BtITBI {Zt tZsj tbB,R WZsj ]B8}Zs$Bt ; nnT;(x >EH <s$RBt < ytBIZ{$Bt B 3B8sj NstZs qYBk VII$RBtTGRjk isI$t sRR w dM D  >H y,B8s W _Ik{9 G stI <$Bs dn eR$8s$Bt BP PZ99k js$Btsj 8sT $- Ak ZR$t }BAsA$j$R${ IR{t 8YBI 3Z99k 7 7kR8R x nnxTn; >MH GsBZR iN stI ZYt p d1 ytIZ{$Bt BP ht$TRs jstZsR ZR$t R{BtITBI {Zt tbB,R WZBtsj ]B8}Zs$Bt ; ;(ET;d; >H t  pBBI8st i stI 78kY _ dn Nst$t ht$ Rs 8s{Y$tR b$Y RjPT{jZR$t {Zt tbB,R WZsj ]B8}Zs$Bt x w E D  ET( >d(H t  pBBI8st i stI 78kY _ d; *$R{ {Zt tZsj tT bB,R PB s8s${sj $tPt{ yeee qstRs{ WZsj WbB,R x w 1 D  n1(Tnn(