Inductive Methods and Contract-Signing Protocols - CiteSeerX

Inductive Methods and Contract-Signing Protocols Kanovich Scedrov
 R.

 Chadha   M.   !"#$&%  ')( (" A.  '*(+,% - ./% 0 University of Pennsylvania

ABSTRACT

1 #2,435 ("("6 879:;'*!$*k(" #$O("-5 .,$*(; >$UJ ‘    t w 0 !x^[u. "')$*$U2’("- . ./"0 “5,2 o  o 7X”N• ‰>– w ,'* ‘  ("'*(H 2X'* ‰  ?j'*9~m  L—=( ˜™ • 1 #, ™   šJa›ƒ0J#Jaœœ! ™pw r 1 #, ‘f‘ •hJa›ƒœ  X5,2 ™pw rPL#, ‘f‘ •››ž!%

$*0^>,"# f=5/p("'*L 0 R $*$*2RZ5/" |f ("$*0

5,2; _"-(H0 ; 'U# >. "a2,%mŸ[ '*(n(40(" '*L;5/-n("- # .,$*(;T. $*'*0 g%`„ ?j$n $U2 ("'*(;?O("- #i., $*( ^f(f'* 'U')0 '*6€U0!lœ‚g-("')L=;v 'U(H#N 'Uv '*,$&% 7XT ,$*2, o (> o '*$*$€ œ‚[- ("0 8. 0 '*0R5 (H"# '*  iTv  'U JK(H#>T!  $q# . > Z >., $ '*P€U0‚q'*(f?&'U0% „N =!'* Y?(H2 TT ""28 ("'U#5 $*X'*W '*(H"'*5 - 0 Y J "#h("')L '* Lk^f(f') ,'*v 0 ')6€U0‚ˆMO>?j'UZ.,$g'*(f(') R 5/ @A B!C D E FG"DD 'U?V [,2k(H#LZ?lZ. ,$&!'*O'*(_'*T./("("'*5$) ?jh,2T. "'*'*. ,0(2Q`,k5/N5$*N>.h=R-("')  # $*$*L O OQ\ (n f./0^[ ];# ,("Z5/ a^[=T.$)"J '* L>  ,"# Z |5/"'*L='U0%h¡ ‰ ? '*,"-  [#(f$U2 v 'U$U2T,2b(H . (! 'Uf'*(f`("0¢,- Z?4?j'U  ("([   N $U2bV^_`./("("'*5 $*-T(Mm'U [> h'* ( 8$*') £,"# |5/u. "'*(T'*98$*'‡ W,"# 0% ¤ „N5- (" Jˆ?‡  ("(R'*(\'*T./"#,T. ./ "a2W?;,"# ("'*L J '* L % ‰  0 l("- ../("f O„N$*'* b¥O5- ("h;.,$  '*( { ŠŒq5- (" Jˆ?† %nŸ[  ='Um'*(n./("("'*5 $*[?jn[. "V2,(2=„Z$*')  N("T;./'*!hT! '*` N. "a2, ‘  $*'*  N¥_5 '*([TT'*" k; Z,"#0,^h  0(h„N$*'*Z')(_ O2, 0%nŸ['*( ^[- $) b. - ]¥_5O; '*(H'*  O '*( ,#L,5/0- ("[ f'*(_ '*("; ]„Z$*') h ,(n m0$*$U2>^f,n("'*L= [ ,"# m^h'U ¥_5I5 -Z $U29-("`¥_5g} (Z^h'*$)$*'* L ("(NT("')L9TL')i$*#L ?jp   h,"# h^h'U ‘  $*')% ˜ -9'*¦'*t '*(9. ./ I'*(X£(H- 2yW("')x?T5 - ("J ?†  ("(b?†RiV^[JK. "a2Y. '*T')(H'*9 ,"# "JK("'*L'* L8. J $f("$)'*L!$U2Y!'*("0 P?†¦€U0!N0œ‚ˆ%YcP| .k R=-$*'*(" "J  ^f'U'* L?j$*'*("§?j;.,$n $*2 ("'*(b€ ¨‚ˆl^h '*#I © (  Ta^[i5 ("')|("("-T.'*(k?h  o $*,Jˆ_IT!  $€U0ž!_ž! ª ‚ˆ./"?j 4 "2 .L#.,2- .$) ^h'*`   T'* '*(H'*mbJ . - #'*£W 9. "? 9'*,"-  0%tŸ[  ("i("("- T. '* ( .!') TP') 0$*')< 0 P(" "'* L9'*8^h'*P. ,$[ $U2 ("'*(k5/J T(f$)'*$U2R"# #5 $*% ˜  R?N X '*("'*(T'*(b 0^«6T! $f '*(" (HT. "'*'UJ . ,(%cP`T! $4V^_|!'* (N?[ '*(" (H;. "'*'*. !(% ˜   '*(bY¬ D@0­® ¯8°zjCH± Š {lDC Œk. "') '). ,0n^h '*#W5/  0(> $*$U2 5 - T'*($U^f2 (b0 2YP. TT("(L(T?†² |  a^[  |#; b?j- "  Z. "N')| ;.,$&%[c8`$*("R '*("-("( C Œ G Š {,³® ¯I°z†C"± Š {lDC ŒZ. "') '). ,Z^h '*I(" (N'U(N. ')`2( ^h'UY  o $*,Jˆ[I'*!"-  k.'*=I R  - ')Y?Z  .,$&% ˜ 8R  k  lq^[R("("-TT > b"-(H0

 'U# I. "V2I'*(^_$*$UJa5/  00 i i ,(p. $)2I `$*=?[ . "V2R'*, (H0 X'*|("')L '* Lbp!"# 0% cPT?†$*$U2P(H#X P. |9 ("'*d?N5- (" Jˆ?‡  ("( ("'*T'*$‡T6X ("'*£("-LL (H0 £'*€U0œ‚ˆ%uc8X0$)$h-T"J ("'*t?`I../"V2u A#@®*@{/Ž#D . ./ "a2,% ‰ u. "'*-$)0 ("("-T'* Li k R'*!"-  k# (b$*28v  'U$U2Y,2P(H.(

 T f,2T N., $l. "') '). ,h b h"- (H0 b'*#

. "a2yi  (H$*2£?j$)$*0^h'* Ld i.,$&Z^[i.I 0 Z,2(H#L;? . ,$&  N f.,$g. "'*'*. ,0  Tp(H" L$U2= '*("  (HO! ,(n O 0_5/=f./^_  `T. $* f h,"# _(]^[$*$l(] h./0^[ O`5/"['U0% ‰  '*(`^[2,4'U? ‘  $*'*b0¢,- (H(>,2i. "'*- $)k-T4„N$*'* ^_-$‡ | Z5/;5 $*;=L- #,`'*0% 7X|. '*("$U2,q^_R!'* ^…Q>} (>./^_ >i5/"=(=Q>} (k5 '*$UJ 'Ua269. ,;T("-  ("(H?j- $_T.$)')P?fb!"# k')  $*'U'*8^h'UI >'*,"- 0/L# $*("(;?] k') (;?O   8¡&  (H¤b. "'*'*. ,9 ui '* (9?>9"- (H0

'U# 6. "V2,% w ')T'*$)$U2,^[T!'* ^ Q>} (`./^_ `9T. $* =  ,"# [(OQ>} ([5 '*$*'UV2=;. ,n Z5/"['*T$*'U'*^h'* ;'*!"-  0L# $*("(N?m ` '*(?m; =¡&(H¤ . "'*'*. ,  `') (h?m"- (H R 'U# R. "a2,% ¥O0-("_-(" "'* Lh'*(q(H2   - (4 ;[. "'*'*. ,q0J T ,"$[X '* (=?N T. "') (O^_|#R|!'* ^  ` T $U2Y5 '*$*'UV2e k9. "'*'*. !k (`')(` ='U>2 # ,("N;v Z; "#'*R("-5 (" O?'U(_$*$)0^[5 $*; '*(f_,2 (H#L9?|. ,$ Y ./|6   T'*R|-T '*e ^f2,% ˜ - ; ("'*6?[5 -(" Jˆ?†  ("(^h '*8("("-T( ?j'U  ("(q295/k(H#0 i0¢,- '*$*,$U2I'*e T(N?_ "#'*i J  -("'*]../"') (q?!v 'U]" (^h'*;^[].]5,2p'* -  '* T ! (%[¡ˆr 'U  ("(_'U("$U?4'*(O.0 b5,2k') - '*h.,?T  J ! ([(_^[$*$&% ¤ ‰  - '*fT  ! (]^_ Z'),"! - 0 T'*I€Uƒ0‚g

-("0 £T| ,$*2W'* € š‚ˆh5/W')W X $U2("'*(?p("')T.$*  . ./ "'*(Z?m-,'*0'*X., $*(k€ ª  ‚ˆ%  Z- (ZT.  ("'*^h'Ub '*(].'*f("'*L')L . - 5$*')h"J 'Uv 0'*8 2I. 'U0% ‰ e. "'*-$‡04?†; >(H;?f|("  '*8'U? ^[k(2I p—Q — ^_=T06,2,k p./("("("("(;  .'*p("'*L '* LT2|?nQ>% Ÿ[ ., $g- ("(h> "2 .L#. '*p.'*T'U'*!‹ G#z @ Œ D`Ž Š { E Œ G"@Ž Œ Cz)³{/@ Œ B!G"D ¡ ‘ w ¤h'*!"! -  |'*8€U0‚ˆ%Oc8p^f'* ¡ ¤ ?†p>. '*k,"# ("')L -=?  X,"# ; ! eq'*, 0 i?† ^h'U8("./  ` `%Ÿ[  '*|../"') (Z?n.'*p,"# Z("'*L - (M ¤ ¡ p¤_95/;T. - 0 R5,2 % ª ¤mŸ[ h')(O. 5 5 '*$*'*(H')Z./$U2  T')$ f'*Tf$*L'U  >("- #|  ¡ ¤ ;'*? ¡ ¤%“Ÿ['*(9$*L'U  0y5/I-y5!2u,2 5/! 2 ^h = 0^h(hp. -5 $*'*; 'Uv '*9 2 (f?    `% ¨¤ u0TT.- _¡ ¤q("- #=  ¡ ¤ % ™ 5/! 2d  T   0IT.- ("- #X  ¡ ¤ % 06 'U?†2i^h   >'U;^f(` 0 85,2 « 6("'*T'*$‡$U2 0P 'U?†2i^h   >'U;^f(k00 65!2 % 0Y$*("I 'U?‡2 ^h   Z'Uh^f(hL  #0 X5,2  k% š,¤ 8 ! " ¡ p¤Z'),X| ,') $O '*L'UJ #$4("')L - ¡ I¤%ZŸ[ >')(b.5 5'*$)'*(H'* JK./$U2  T')$ '*T]$*L'*9 _("-p  ¡ ¤ ' ¡ 9¤% ™ 5/! 2T  O  T.- ("- #   ¡ ¤ % œ¤ s0W  " ¡ p¤`'*!6e '*L'U#$f("'*L -  ¡ I¤%[Ÿ[  `'*(pb. 5 5 '*$*'*(H')Ja./$U2T')$g'*T`$UJ L'U 9 6("-W  ¡ ¤ 9' ¡ I¤% ™ 5/! 2e  ;  0PT. - ("- #|  ¡ ¤ % ˜ -O?j$*'*Tk- ')'*i#  $45/ V^_I (" V^_I. "') (% N^_ `T., $_. "'*'*. ,(k T(". J #T T=- '*0')6#  $*(`XŸ%mŸ[("T  $*(`(HJ ("- T XT5/R¬ G#z Œ D E ‹ G ŠŒ D"Ž Œ D"° m'&% %*l 5/! 29 .Z  “

 `. "'*'*. !¡&;!2 5/! !2X^h ./("("("("(p `. ')`("'*L J '* LR 2I?O=. "'*'*. !¤h0i^f'UbI')(  $&%>r -"J  Th ("N  $*(h("("- T >5/kŒ GH@{ C ‹ @G"D{ Œ   #  $N  X$*("(9YT("(LN- $) ("(Re'*, 0 u. "a2 0 (b'U f 8|'*,"-  =d5(" RT("(L(=?† '*( #  $^h'*- 5$),#!'* LR; $)2'*L9%fcP>("("- Tk (H2   - (`T=- '*0'*eT!  $ˆ%c8T 0=$) 6   'U'*X?n.'*p#  $*(N(h(H#0 X'*6€*‚ˆ% d'*(]("("- T >'*!#'*=./  !m #5 ("f? #b?  N.,$l'* (H# (O ['*[ ([ 0 - ./5/ ?j% ‰ R-  $U2 ("'*( ^[N?j-" Z("("-TN 

, (f hT'*("5/ 0p

, (; > >(`R. "V2I||!"# 0% ‰ £€U0œ‚ˆ4b-  ( $*$*0^[0

b5/;')  !$U2|"-.0 T$U2R; #5 ("`? \^[([!'*("'*5 $*N` Z'*!"-  0% w '* h^[N 0h$) 0 T Z J '*9?m.'*p#  $*( ^_` T$*$)0^  ;')  !$U2R"- . 5/ !'*_? `,5,2=!')L`$*$/T=- '*0'*=5/ V^_T'Uf

 . "'*'*. ,(h5 ("5 $*p= ;'*,"-  0%

 

 
! " $#% #&  

 ! " $#% #' "(  (*)+-,  (*)+-, " .# #/ #&0#  2143&,657+  1  " $#% #& 8  2

 19:;="? A@ " $# #&  (*)+-, " .# #/ #B0#  C1D3&,657+ 

  (*)+E, " .# #% F#&0#  G1H3&,657+ $

I

C *

! " $#J #B LK ="? "  (*)F+E,  (*)F+E, " .# #BM#  !143&,657+ ON  1PK ="?Q "   (*)F+E, " .# #J0#  R143&,657+  ! " $#J #B   ( >="? " S(M)+E, C(M)+E, " $# #J0#  T1U3&,657+ ON .  1V  ( >="? "  0(M)+-, " .# #J0#  R143B,W57+

TX



/Y

EY

THE GARAY-JAKOBSSON-MACKENZIE PROTOCOL



2.1 Purpose and assumptions of the protocol







c O0^Y  (" '*5/[f.,$,5#'*0 ;5!2pZ("$*'*L,!')("'*k? 8 fV^[JK. "a2b.'*T'*(H')Z!"# "JK("'*L '*L>. ,$/? 1 #2, 35 ("("gm e79:;  cPk '*("-("(p b 'U?†J ?† (p'*i- p.,$] X  ("=.,$*(p'* w   '* ª % ¨ % ‰ T Z., $&Za^[>. "') ([2T,# f;"- (H0 b'*#

. "a2,h  ?j"y ?j " ud( `% c8i(H#"|5!2u  (" '*5J '*LZO.-./(""2. L#. '*_("("- T.'* (Tk- ')'* T! $g-   [^h')#Xp.,$')(ZT0!_b5/;  - 0 g%











Z

T

[

  |(H(h ("$*-'*g%

2.2 Protocol Description

Ÿ[P.,$` ("'*(H(i?k6("- 5 . ,$*(M D
Ž#±@{,³,D  @A Š G Œ&n GDC Š ® D ("- 5.,$*(%T”N("- $*$U2I k. "') (p^[-$)

""2X|'*` `,"# ;5,2X -'* LTk  #  L>("- 5 J . ,$&%hŸ[  2^_- $) 9,#  x- ("'* Lb `?4 ; hV^_ ("-5 . ,$)(9^hy  2u '* £("T ')Ld')(9T'*("(% ˜     2Y,# T'U0]  2P e$) L T#R. "T'*W|#  L ("-5 . ,$ˆ% ‰ 8 . ,$f ("'). '*m^hd9. "'*'*. ,=Q«(" ( 9T ("(L kCCH³ '), 0 i?j  Tm'Uk^h'*$*$[5/R55!')0 8( Q SM kCCH³ %   ‰ >[ (" '*.'*g_V^_N. "'*(m^h'*$*$ 5/[ ("'*L 0 k( ;'*L'* p k  p("./  !0%O¥_?j>  - '* L= . ,$&  N. "') '). ,(Z;("("- T0 T= 0;L0 R- ./ #k  0} (m') ,'UV2,0_,"# - $ !  p _') ,'*a2 ?` 9"- (H £ 'U# u. "V2, >% „N(R'* €U0 >œ0‚ˆZ^_e Y    ("')  ` 0^ ')(')(p# '*0 lg')e- ` $U2 ("'*(% ‰ e 'U')  2=$*("=LZpL$*5 $*$*2b-  ')¢,- f') ,'*v   n5/ ?jZ 2  -i i.,$&% o ' l,9'* (H# (|?> i.,$ ^_-$‡ T N ' l ,_') ,'*v  (%qc8h?†-" f("("- Tf O '*,"-  `! 0^h(; '*(;') ,'Uv 0%       ;% c8;5/L'*95,2R (" '*5 '* Lk ;  # Lp("-5 . ,$ˆ%

'*(". $)2(h'U(ZTT'UT,_  "!$# %&#'(#*) M ("'*LW5,2e(" '* L +¡  ¤m'*, 0 6?† k% ‰ ? … J  '*(['U0,  R'U[ '*(". $)2 (['U([TT'UT,n5,2b("  '*L +¡  ¤'), 0 p?† % ‰?  '*(m'U0'Un(" ( +¡  ¤ '*, 0 X?† >% ‰ ? ’ '*(N'*0 '*(" ( +¡  ¤h'*, 0

?†  R p. ,$v '*(" (f?j >%_Ÿ[;.,$gv  '*("( ?† ^h9'Uh'* ( +¡  ¤%OŸ[ ;.,$4(H. (Z`  J ("')5/ 9(  …M -, .¡  / ¤ 0 M 1 .¡  / ¤  …M $2 .¡  3 N¤ 0 M $4 .¡  / N¤ 2\0¢,-  (H u5/"I 5 6# !$%7""!$# %8#9#*) M . ,$b?† e'Ui(" ( +¡  ¤9 x5/ ?†Y'UI J  '*( _+¡  ¤%§Ÿ[ '*(I'Ui , (I5!2t("  '*L :, ¡  ¤qb Z.'* \#  $&% ub '* '*L 95/"b0¢,-(H0_#  !(b'U #5 ("I Y# #!(b'U?'UT (   R(H^[  \60¢,-  (HT?j?   P 'UT ')0 u5/ ?†I  ‘   $&% ‰ ?4'*[ ( 'Uf^h'*$*$gf("  5 #,2! '*L   "^h'*("k'*# (N'U?O'U (Z("$*@

 |5/ ?†% ‰ ?]'Up (l'U ("  (` (H0 8("$*- ') +¡  ¤ +¡  ¤% *,#¤f 9("  (Z'U ˜  "^h'*("k'UN'*("("- (I5/"  (A ¡ > Y#    $ˆ% ‰ q#'*("(n'*(q5/"m© Lh?j   p >(H( b5/" g%;„Ne5/" i'*(;.T'*("k5!2   ;'U  (h N ^h'*$)$ Z ("$*B   T'*X?†--% c\ '*$* d')(4 q$*$*0^[0 `N5/"0'Um'*(m$*$*0^[0 ;¢,-'*45/ ?j 'Uh ')(f pv (HhT ("(L% 2R0¢,- (H T("$)> CED&#*)GF*H"!$# %&#'(#*) M . ,$q?† N'UN("  ( +¡  ¤[ R5/ ?j>'Uh ')( +¡  ¤% Y2h- p]("-5 . ,$,?‡ q'U(" ( +¡  p¤[ R5/ ?j>'Uh ')( +¡  ¤%  0¢,-(H( x ("$*` `.,$m'* (H# >5,29(" '* L ¡ +¡  p¤ +¡  ¤"¤% e'*!'* LX= J ("$*|0¢,-(H0]!(k'*?N'Ub (b T (H^[0 £90¢,-(H=?†  e k'*> ')0 Y5/ ?j|P  …  $&% ‰ ?Z'U= ( 'UN^h')$*$mp("  I5 X,2! '* L / "^h'*("='Up# #!(N'U?O'U ( 5/"0 9("$*0I

 5/ ?†% ‰ ?n'*N (N5/ i5/"0 9Z J ("$*0 95/ ?†; X'*Z(" (h ;(H0 9  '*("')iX #  $&% ‰ ?'*h (['U  f5/" | [("$)0 . ,$ˆ 'U`! "(  +¡  ¤ [+¡  ¤Z

("  (N'UpI “  $&% ‰ Z#'*("(;'U(N("$*0 I©/LT?†



˜ } (f("$*;("-5 .,$'*(Z("'*T'*$)0%

% S ‹  J?KELNMGO:MQP*MQRO ª %)T @ G Œ zˆŽ z ‹  @ { Œ
U Dz Œ ± DGWV Š Y G X[ZTzjC`C@zˆ° KŒ Š ¡+ ¤_Š G ¡+ ¤]\ ±@ Df@ @® zˆ°pŽ Š { Œ G"@Ž Œ z F]z Œ  ± @C[Dz Œ ± DG _¡+ ¤;Š G _¡+ ¤ @{ °XDz Œ ±D G

W 0

0





ON

1



ON



M

! 8#J #&  @ 8# #&

K ="?  R

:K ="? @ :

K ="? @ 2 T+ /1 L .#B2# #/ F#B #% #&

2 T+ 1  @ $#& # #/ #B # #J 2 T+ E1K =?Q $#& # #/ #'

2 T+ E1K =? @ .#B2# #/ F#B   8#% F#B  1   @ 8# #J K ="? " 6,-3# > (Z

S

K ="? @ # #J



>

MK ="?Q

M



*K ="?Q * 8#% #' #  @ 8# #J

 @

  (S

 (S

   ( >="?Q

(G

#*  ( >="? @

ON









-

0

 " .#J #B



/1  L " .#J F#& F

1:K ="? " 6,63 #J .# #/ #& 1:K ="? K "= ?Q " W,-3#& .# %# F#& T







+ /1  L " .#J F#& + 1  @ " .# #J + 1 K ="? " + 1 K ="? @ " K ="? @ " " $# #/ #B



R R

R R









R + :  R T R T



(Z

(0

  (MK =?

‰ T'*L') $g.,$]€U0‚ˆ  Z("$*¢!-(Hf ("'*(H0

?n>0¢,-(H'* LT. "V2l} (("'*L - ki`,"#; X  .'*R,"# b("'*L - X?h|  =. "a2,% ‰ y€Uœ0‚KO  -  (=(" 0^_0 P =W') ,$U2Y"- .  …026$*0 P $*("(k?f?&'U ("(%9Ÿ[  26("- LL(H0 d|v8'*8^h'*8b("$* 0¢,-  (H ("'*(H0 9?O. '*> ,"# N("'*L - (?n5/9  . "'*(%bcPk#> '*(pv  0 i.,$O(`- ; ?j T./'*!  X ')(" - ("(Z-Z ' l   (% cPZ ')(" - ("(_5 '* © 2> Z ' l   (O'*T-O.,$ ?‡’   ("'* (h?m 1 3,7 ., $q(Z  v  0 R')6€U0 œ0‚KM ¤_c8p("("-Tp./ "?† Z "2 .L#.,2,,^h '*$*>'*6€*‚ˆ p "2 .J L#. '*i.'*T'U')(f6  v 0 d')£ T(T?;. 5 5 '*$*'*(H'* ./$U2  T')$l')TT.-#'* (% ª ¤ncPN("("- TZ^f'U JK.  0 R T"#(". ,[#  $*([5/J V^_Xp. "'*'*. ,(Z `')(H0 |?m. ');#  $*(% ¨¤4c8f  . $*'*'U$*2k'* $*- [ f') ,'*'*(n?/ f. "'*(n')!$*0

'*9 ;,"# N'*I "2|T("(L; N'*(N5/ ')LT(",0%hŸ[ '*(Z'*( '*T #   Z^h'U=[^[$*$UJK(H#5$)'*("0 T.#') f?l'* $*- '* L  T. "'*'*. ,(}q') ,'U'*(`'*P0#P(H.8?ZX "2 . L#. ') .,$&%]„Z$)(" , 0^d0=,"#O'*$*-  (nL$*5 $*$U2b- ')¢,-  ') ,'Uv 0% ‰ i b. !'*- (pa^[9 ("'* (  k^f(`X("- # ') ,'Uv 0%=cPb ') i'*(;5/0-("T5/W€U0 _œ‚_$*$*0^’ =?†$UJ $*0^h')LT(" '*M  x""2b("'*Li= ,"# h^h'U9,"# h ! 

"- (H `'*# ;. "V2, `% (" ( ¡ ¤'*, 0 p?j k%hŸ[`'),"-  0   ?j"I0$*$*0_

^R$*')(H  (Z9 `#    $ 5/ a^[  k%  M -, ¡ ¤ ^9'*, . (p'U0% '*T(p-p^['U'* LR?j>T.$*2, e¢!-'U(% ("!( ’?j=P5/" g4^h | ` 0!')L98,""2i?j  ,"#N5/?j '*("("- (h p5/"  % ,  ’M ¡ ')k'U(O #5 (" ?j9 '*(P¡ p¤T(" (X85/" \ %     (XW$*') y,"# I

 $U2t 5/" gN!- ( !'*$)'* Lb?j'U  ("(% š,¤TŸ[9.,$(.(" ! £'*€U0‚p(" T(bY$*$*0^ s 5/T!# 0 Pk- $U'*. $*b'*T(`5!2e0Y. "a2,%9Ÿ[')(>("T(; !'*$)iu. '*T')(H'*I(" "'*L8("'* ie$*'*'*-(R. "'*'*. , - $) £,#  k- $U'*. $*')T (=?j'* LP'Ub8 e  ./ ("'*

#5 ("p("0(%mcPZ!'*("N Z.,$l(">  t(f $U26 =¢!-(Hp?‡ 06. "'*'*. ,;?j`0#6-6?[ 

.#&2# #J #&

  (  ="? #  (  ="? @ 7K =? "  

K =?

2.3 Differences from the original protocol



N

  (MK =? @

Ÿ[ b-(p?_b'*L'* $]., $Z€*‚]$)'*T0 e(" #$ . ./ "'*('* $*- '* Lf?&'*("(m `5- (" Jˆ?†  ("(%4cP] '*("-("(    (";../"') (Z'*9("  '* (œk Iƒ,%

>

G

K ="? @

0





X









. ,$&%_Ÿ['*(f(" -$) 5/N(" ') !_5/0- (";# '* L`> . ,$n  v  'U'*I0I. "'*'*. ,'*(p$*$)0^_0 iT ,#   $U26  % 26 ,# >'U`?jbd5/">b| ("$*% 2R!# Z'Uf?jk("$*%

M



3.

MULTISET-REWRITING FORMALISM

Ÿ ;.,$4?†$)'*("s^[`-(";')(Z=-$U')(""JK^f'*'*Lb^h'* [ '*(H,')$ ¢!- ,'Uv 0'*,7 w •`,(_ (" '*5/0 b'*I€ ¨‚ˆ%mcPf-"J $*'* '*[  N $U25 ')© 2,% ‰ ([(H2 !#'* $*(_T(,?&(h

-$*(% ‰ ?f =^[,(;X. (",>X(H2 (H '*6'*(>#')  95/ L'* (b5,2Y# ,("'* LYi,05 - $)"2,_ G#C Œ E Š GH°,DGICz)³{/@E Œ B!G"D Ÿ[ '*(O')(O;(H# # b'*b?‡ ,2!JK(""0 k$*L5 #; v(H"JK# m$*L'*%]„Z(q- ("- $& NŒ DG#=C  nZ("'*L -__ ^_$*$UJK?†T0 e  .("("'* (`.! - 0 i5,2i.. $U2 '* L|?†-  '* (p L-T,(f?m "N(""0%O„ F@Ž Œg'*(Zkv (H"JK#  NT'* ?†k- $)6 TX# ("u("'*L - [^h'U -T?† I'‡5 $*(% Ÿ['*(NT0 (f Z=?& '*(f p ("- $UZ?].. $U2 '* LT=. 0 '*0 (H2 k5/$OIL- 8 T(`?hR " =(""(%6„ C Œ @ Œ D '*(k k- $U'*(" h?m?j (`¡ˆ$)$ f ;(Tp("'*L -0¤% „t(H#p"# ("'U'*|')(h GB ®)D ^f'U"X-("'* Lka^[bk- $U'*(" ([? v(H"JK# RT'*X?†k- $)(h W  ')(H !')$¢,- ,'*v 0'* '*Xp(H2 ,# '*p?j ,

 , , l%[Ÿ[ `T0 '* Lb?n '*( -$*e'*(R R'U?>("Ti(H# ,#'*(|?& (X5#')0 \5,2£ L- p("- 5(H'U-'* =?‡tv (H"JK#  4T'*m?j=-$‡( , !>   d./("("'*5$)d !6(H#d')(i Y(H#  e'*( , ("'*T'*$)k n5-`^h'Ud?j (k5 #'* 0 P5,2 £?†  T0 u £?j (R5 #'* 0 £5!2 t?† ,   g ^h  , ]. $) 0 >5,2; ^P(H2 k5/$*(% ‰ ? _O?‡ ')5 $*(;'*ek-$) ,

 , , g ("9|"00 W(b- '* ($)$U2W¢,- ,'*v 0 8- L - = -$*% ‰ \y.. $*'*0'*\?>6-$*[  ("I'‡5 $*(R2d5/  . $) X5,2X,2|L- | T(% „Z(`6 T. $* ("')  `b(H#n
¡ 4¡ ¤"¤ >¡ ;¤+,4

-$*/¡ ¡ /¤ * T¡ 4¡ l¤ ,¤ ¤%n„u./("("'*5$)h !O(H#f'*(O5J #'* 0 p5,2p'*(H#,')'* Lf q-$*] ¡ 4¡ ¤"¤  T¡ 4¡ 4¡ ¤"¤ ,¤%]„N.. $U2 ')Lk')([-$*!^[p# ,("`=  ^t$*-  ?j =

 . $) ¡ 4¡ ¤"¤`5,2 T¡ 4¡ 4¡ ¤"¤ 0¤%WŸ[ '*(TL')(T- (=|(H#
T¡ 4¡ 4¡ ¤"¤ 0¤ >¡ ;¤+,% „Z(.(",0 W'* € ¨‚ˆN8.,$"2W ("'*(H(R?;  . "(M£d5/-  0 \. ("8 (" '*5 '* LW.,$;'*'*')$)'*( '*'*')0g("./  0g$*'*,0g;("  ¤ eR '*( H'),;- '* ?T5/- 0 y("- 5'*(9 i0x #  '*^h'* 'Ub. ')R ')L'U#$f("'*L -X 8 R"("./ ')Li. - 5 J $*'* 'Uv '*P 2 (%”("- $*$*289 ')L'U#$_("'*L - TY|T(HJ (Lb'*(;T. 'U; ("'*(H'* LR?_RT("(L= 9k("'*L - = 6T ("(L%…Ÿ[6("'*L - 8'*(X-("0 ud 'U?†2£ e./ (" ^hd')(|("- ../("0 \Y 0iL  #0 y'U0% ‰ y- X?j$*'*(" PT ("(L 4h("'*L0 u^h'UtP.'*i 2 9'*(9  0 u5,2 ¡ l¤h^h  T'*(k"("./ '* L|. -5 $*'*k'*v 0'*  2,%9Ÿ['*(= #'*g]$*$*0^h(=- (`9T! $OT 'Uv 0'*Y5,2 . " 8# '* L % w q?†k T. $*9. ,$_. "'*'*. ,0 Q`^hX'*(p^f'U')LX?j>|T("(LT("'*L0 6-  ;R 2I^h ("






9 E#    #/9 (  L     E#   #   A9 E#    9   9 #  E%9    E#      9 E#   #%9T(  L 

Q  E#  E #   (

"! 'Uv '*i., ("(%`Ÿ[ '*(N 'Uv 0'*e5!2 . " y# '*LP'*(X("'*T'*$‡XPe   "2 .'*y5!2£. "  # '*Lb(h. (",0 |'*P€ ¨‚K% ^h'UP.- 5 $*'*T 'Uv 0'*8 2 m 1 '*Y|. "'*'*. , . "'*'*. , “^h'Ue. -5 $*'*> 'Uv 0')i 2 > iT"-(H0

 'U# p. "V2, 6^h'U`. -5 $*'*] 'Uv 0'); 2 # ¡ ¤ ^h'*$*$ 5/_ 0 ;5,2 ¡ ¤% _¡ p¤ 5,2 n¡ H¤

¡ I¤l5,2 ¡ I¤%

K ="? ; - #$

;-Q#/K ="? ;-#%



.;0/ :

;1  ;2  " $#% #&   ; / J# $#%;1W#%; 2 9:;+ >="? L@ " .# #B 9:;="?  ; 1 #J .&# ;0/Q#%;2 :  ( >="? " :3%K ="? ;2%#J;0/ #

4. PROTOCOL DEFINITION IN MSR

cPT0^s '*("-("(kT.'*("|  v  'U'*Y?ZT.,$f'* 7 w •`%mr> T(|?h!'* m^[- ("("TR5 5  ')J  '*(M ‹ °   _¡ ­ H‹ ° ­ { ­ ­ ­ ; TD ­ ¤ D _¡ ­ H‹ ° ­  ¤  ¡ H ‹  ¤  ­ D C#z*³ ­ ° TD Cz)³ ¡ ­ H‹ ° ¤ T@ Cz)³ ¡ @A Š G Œ "‹ ° ¤ =G  TD D ; @A ŒKŠ ­ ¤ p% Cz)³ ¡ ­ T@ ¤, G"DC Ž { tŒ Cz)³ ¡ ­ ­ H‹ ° ¤ Œ C#z*³ ¡ ­ ­  R') ,'Uv (Z >.,$m'* (H# % O'*( eT(HJ , '*(b I5/"T0¢,-  (H0 (LI?N 9  #  L|.,$&% -,'*(T 9("$*90¢,- (H|

¡ ¤%  (HZ. "'*'*. ,(TL(Hh  ("`^h'*$*$ 5/i') ,'Uv 0 \5,2 `Š {/DC Œ B!¯ ¡ ­ ­ ¤. 0 '*0(9 u^_0!$U2

'*("  (H_. "'*'*. !(m^h'*$*$ 5/f') ,'Uv  k5,2 zjC `Š {/DC Œ B!¯ ¡ ­ ­ ¤#% w "L$U2| '*("  (Hf. "'*'*. ,([^[-$) |5/') ,'*v 0

5,2 @° D¯ ¡ ­ ­ ¤b.0 ')(%¥_u 2 (T'*u   < . '*0`;! 0^h|=;'*!"-  0% t$*("T,#'*( ¡ ­ ­ ¤4. '*0 (q^h '*>') ,'Uv  (q"- (H0 ; 'U# `. "'*(q^h'U .'* . -5 $*'*Z("'*L '* L> 2k. '*(N¡ ¤%r -" T   2`. 'U(]T L(Hn 

£. 0 '*0(]f. 'U"^h'*("

'*( V'*,0%“Ÿ[ i.- 5 $*'*$U2£ -  u 'Uv '*\ 2 (R?;  . "'*'*. ,(kR    85,28Q P¡ ¤p.0 ')(k 6  . -5 $*'*$U2T  - 0 b 'Uv 0'*2(]?g"- (H = 'U# b. "') ( `  0 |5,2|Q >¡ ¤_. 0 '*0(% §$*("£,#'* ( Ž Š { Œ G"@Ž Œ¡  ¤|. 0 '*0(X^h')#t') ,'Uv ( !"# Z !(%fcP;?j- "  ("("-T` h `'*,"-  Z 0^h( $*$g ("p ,"# h !(% Ÿ[ N7 w •u  v '*'*T("')(H(]?N$*NL  #'*., $   '*(Z?  k   ;'*,"-  [  "2,%

1 # 9;< 5 # @7 1 A 6# 7

 3 W; ,W+WK  D

I# K SR F 6I # 6 - *) D

# 43 # 5 # 6 1 9;< 43 # # 5 # 6 = 1 87 : # 3 # 6 > 1 3# 5# %? 1 /# 1 7 1 87 # = 1 6# 3# # 6# 5#  +(B = (Z3$C   Z T,  ED GFH9 JI # K LFH9 JI # K - ; , #%;- ZX :M %N I# K 'OQP M %N  T +(U JI # K VD GWXWY9 ; 2*, #J; 2 &FH9 ZWXWY9 M[[T ; *[7 ; 2



4.1 Role Generation Theory

Ÿ[ p$*;L #'*9"2R ("'*(H(Z?n=("'*L$*;- $*M

FH= 9 ¡; /, #%; / ¤ # FH9=¡;1 , #%;10¤ #0WXWY9=¡; 2*, #%; 2 ¤ # Ž Š { Œ GH@Ž Œ0¡" 9¤    H\ ¡+ ¤ #% \ ¡+ ¤ #& \ ¡+ ¤ #FH9=¡; /, #/; / ¤ #FH9=¡;1 , #%;1¤ # WXWY= 9 ¡;2*,E#/;2V¤ # Ž Š { Œ G"@Ž Œ¡" I¤ #]¡"¤ Ÿ[ '*(h- $*;(" $*$5/; ?j"| ?j " XT(M k  % ‰ R p$) L   #')x"2,ZV^_W. '* '*. $*(9^h'*t2y. '*(8¡; /, #/; , ¤  W¡; / 1W#J;0 1 ¤Lb-./eR ,"#  !:6 g')  !'Ua29?O  "- (H 6 'U# 8. "V2.; 2 n P9L$*5 $*$U2P- ')¢,- b')  !'Uv  0 m  % Ÿ[ Z- ')¢!-  ("(_?g'*(_L- #,0 5/0-("N'*(H,')$l¢,- J 'Uv 0'*\T0 (bL #'*\?`6?‡("u$*- %tŸ[ X"-(H0

 'U# R. "a2l} (_(H#;'*(f'* 'U')$*'* J  '*0

2kp(H#')R^h '*#X'Uh (Z(" ! $2% 1   "("./ (`IX(H#T'*8^h '*#P'Uk (; ')0

4 %  "("./ (f=(H#;')R^h '*#  (f')("("-0 XI5/"f J ¢,-(Hn \

, "("./ (Opf(H#h'*b^h '*#T'*] ( T5/" k?†n '*(m0¢,-  (H]

,n"("./ (m (H#'*b^h '*#'*O'* ([p("$*- ')R?†O '*(O0¢,-(H0%  "("./ (f> p(H#p'*|^h '*#  (f'*("("- 0 |>("$*p J ¢,-(H “

.1k" ("./ 9 >(H#(') 1 

^h'*'U[ (n'*0 5/"  Tfp("$*-'*g  ("./ J '* $*2R?jh '*(f0¢,- (H0% Ÿ[T  a^[65/ a^[   …'*(kT! $*0 65,2 . 0 'UJ (%kŸ[ >^f'U JK.  0 I"# (". ,;#  $m5/ V^_ 

'*(hT! $*0 R5,2 ¡ N¤_. '*0 (% „ ^_0!$U2 '*("  (H ;'*  'U') W$)$`?k85/ (H#(]2P. T,28T("(L(k?‡    a^[8'*d,2 ?ee(H#(T P#| I?j- "  =. "b')Y|. ,$ˆ% c8T 0TL')P bT.$)(`?hb- $*(` k$)$*0^«-(> T! $ ^[!$U2R '*("  (H %]Ÿ[NT.$) 4 $*$)0^h( '*9(H#
 0 ª "¨ cP=(" 0^“ `0#8'* (H# =')    -",g-  (g'*(?j'Um p   n m. ,$,')(g?&'*0%m„N("("- T  |'*\ v L-#'* hV^_Y.'*  '). $*(  kh^h (" . '* .- 5 $*'*Z 2b. 'U(fk¡ ¤  i¡ ¤ LN ("'*LX;!"# _^h'U!"# - $  ! 6  Tp"- (H0 ='*#

. "a2,  ^h ("=. ') . -5 $*'*k 29. 'U;'*(=¡ ¤h5,29- ("'*L -$* k%n„W?‡("bL$)5 $)$U2=-  ')¢,- _'‡ ,'Uv  0 |L (nL #

 \^[e 0ed  ^ .,$;'* (H# e') ,'Uv  \5!2  , %nr  

 ] [("-$U')L; v L-#'*T5/ X(H? X(" '*gf- $) ("(T "^h')("I(H#0 g_0# 5 $* , %  v L- #'*(^[- $) ;T0 v L- #'*(0 5$)n?†

N

- 8 0  0 $#J #%;0/Q#%; 1 #%;2

\

E

; /, #J; /



H

;1 , #%;1 ; 2*, #%; 2 W

1





„N("("-T ^[;T





B 8#(N¤

'*(]  (HO \(H"L$U2T '*(" (H0%]¥O2 ¡+ '*9'U(h' fX(H#p^h'UXv(HNL-T,h( 

%

"(

6 D ŒB P1 0 $#J #%; / #%;1W#/; 2 zˆ°D{ Œ z F¯W@ 87 Š GZ@®j® G"D"@Ž#±@A®)D  \ @{b± Š {/DC Œ ±@CfŽ Š bE  B ¡+ 8# (N¤   F Š G =
-=  [+ ;* ! ¡M K ¤ z F  < # =  [? ; ! ¡M K ¤A@  [+ ;* ! ¡M K ¤ z F K ="? ¡;7#$l ¤ Š G  ¡;[#% L#% ; , #%; 2 ¤kŠ G 9:;+ >="? n ¡;[# A#%; , # ;H2 ¤`Š G 3%K ="? ¡;[#&; , #%l ¤  [+ ;* ! ¡M K ¤  B   U73%C ¡* K ¤ zjC Œ ±DdCT@®†®)DC Œ CB ‹ DGC D ŒiŠ F M -K \ CB Ž#± Œ ±@ ŒC< # =  C¯{ Œ ± UW =C Z|z F <  KJU73%4 C ¡M K ¤ @{/°  K  U 7  % 3 C   ¡ *  K  A ¤ @  ¡ 7 ; % # A & # ;  E , % # ; ¤ J # : 9 <   ; + 2       >=?  = ¡;[#% L#% ; , #%; 2 ¤  KJU73%4C ¡M K ¤ z F A#%E; D , P U73$, 4C ¡M K ¤A@ K ="? ¡;7#$l ¤ #B3%K ="? ¡;[#&; ,E#%l ¤  KJU73%4C ¡M K ¤ z F L#%; D #  ¡;7#% A#J; , #%; 2 ¤  KU73%C ¡* K ¤A@4¬ ± DGD ; D , zjC Œ ± DCz)³E {/@ Œ B!GDp­D¯RŽ Š GG"DC ‹ Š {/°zj{,³ ŒKŠRŒ ± DDGz
Ž@ Œ z Š {I­D¯ ;  F G 7 Š G;@`³z  D{iŽ Š {
³B GH@ Œ z Š {  \qŒ ± DpC D Œ[Š FNDCC@0³,DC;@6 @z&®UE H  ¡l ¤ # @A®)D ŒKŠTŒ ± D`z†{ Œ G#B °DG>z†C`°,D
{/D"° ŒKŠ A#D Qk¡  ¤ 1
(I J ¡l ¤ # ¡l ¤ #%. B ¡l ¤ #% Y"B ¡; , #%; 1 #%/ ¤   +  W ± DLKMN(O Š F Œ ± D`zj{ Œ GB°,DG`zjC;°,D
{/D° ŒKŠ A#DP ¡  ¤ 1PKJU73%4 C ¡"[+ ;*! ¡ˆQ ¡  ¤"¤"¤ ¡ > ¤ Œ ¬ Œ Œ    Q†F P ± D{ DkC@¯ ±@ zjC`zj{ Œ ±D  zKD ¬yŠ F;zj{ Œ GB°,DG;zj{   0 R  S C Œ G Š {,³® ¯°zjCH± Š {lDC Œ z†CZC@z&° ŒKŠ ± @W D>@  @® zˆ°bŽ Š { Œ GH@Ž Œ z F K ="? ¡; / >#  ¤NŠ G 3%K ="? ¡; 2 #%; / >#  ¤ zjC[zj{ Œ ± DM0  zKD ¬WŠ F Œ ± DNzj{ E Œ GB°,DGJG  Q Œ zjCNC@z&° ŒKŠ ±@W D`@{i@A Š G Œ ŒKŠ ­D{iz F@A Š G Œ ŒKŠ ­D{ zjCzj{ Œ ±DF0  zKD ¬yŠ F Œ ±D>zj{ Œ G#B°,DGJ ¥_- ("?Zb?†(" ("(>?0£  '*_ m'U>0Y5/T("0^hY5!2 '* -  '*k> _$*Lk?l  '*') (n?0# 5 '*$*'UV2, n'* ,29# 5$*=v L-#') 0 p5/>')Ia^[R © '* '* L (H# (Z?†Z(TB % ™ 0^x^[b  v  ?j'U ("(p?†;(H %pc8k5 0| k  ?‡J '* 'U'*W'* €U‚Z'*!Ia^[6  v  'U'* (%YŸ[ |  v  'U'* (>?jR   (H*

95/p(H#0 X("'*T'*$)$U2,% J?KELNMGO:MQP*MQRO œ,% š % NST3U4UV-*XWWZYX)+!#)+*9XW"3\[ ] 6 D ŒN 1 0 .#&2#J;0/Q#%; 1 #/;
2 zˆ°D{ Œ z F¯I@ ‹ G ŠŒKŠ Ž Š ®_z†{ C Œ @{/Ž#DX@{/°I®)D Œ A#D @{9± Š {/DC Œq‹ @G Œ zˆŽ z ‹ @{ Œ  :  W ± DGDkzjC>@GD"@Ž#±@A®)DŽ Š {
³B!G"@ Œ z Š {  \ CBŽ#± Œ ±@ Œ ± @C Ž Š  ‹ ®)D Œ D"°  zj{  @{/°=±@C;@C  @® z&°RŽ Š { Œ G"@Ž Œ  B G 7 Š G_@®j®G"D@Ž#±@A®)DhŽ Š {
³B!GH@ Œ z Š {C  \/Œ ± DGDhD
zjC Œ C  G"D@Ž#± E @A®)DmFG Š   \ zj{  Š ® 0  zj{!³ Š { ® ¯ Œ ± DpG#B®)DC Š F @{ ° Y \ CB Ž#± Œ ±@ Œ ±@CbŽ Š  ‹ ®)D Œ D"°  zj{  @{/°|±@CRDz Œ ± DG@ @® zˆ° Ž Š { Œ G"@Ž ŒZŠ G>@{6@A Š G Œ[ŒKŠ ­D{=F Š G  zj{    œ,% ª % Š ® zj{C Œ @{/Ž#D  z†{ zF S {± Š {lDC Œ

X

P

 '%8!9 

1 ¤

D"Ž Š  ‹ Š Cz Œ z Š {XhB ®)DC M

P ;]  9 M J ¡  A#$U "¤  J ¡ l¤ # J ¡U¤ 6 X SM ¡ l¤ J ¡ l¤6 J ¡9;¡;2H¤6 74@­D < z*³{ M ¡;1 , ¤ #  ¡ 74@0­D < z)³{ ¡;1W#$ A#%; / #%; 2 ¤"¤ #%T  ¡;1 , #%;1¤ #"QH. . TP¡; / ¤ #"QH. .>¡; 2 ¤ C Œ G Š



\fŒ ± D{

± Š {/DC Œ



L



F

]'%8!9 

 D&

{!³® ¯T°zjCH± Š {/DC Œ ± @Cp@ @® zˆ°bŽ Š { Œ "G @Ž Œ F Š G  zj{ Œ ± DG"D|
D z†C Œ C G"D@Ž#±@A®)DhFG Š  #C BŽ#± Œ  ± @ Œ  @ { ±@C`@ @® zˆ°Ž Š { Œ G"@Ž Œ F Š G  zj{



B Q†FZ@{±

C

Š {lDC Œ ±@CZ@{9@A Š \ @®j® G D"@Ž#± @A®)D;FG Š   Š Œ Š Œ { ±@ k D @ @® zˆ°|Ž { G"@Ž Œ

 

 
 # 6

")G

W







 


(

(

)*'KER'#*K 

7





Š | G @®j®_G"D@Ž#±@A®)DIŽ Œ \ z†{ Š ® 0zj{,³ Š D
zjC C G"D@Ž#±@A®)DOF#G Š  Y\ CBŽ#± Œ ±@ Œ ±@CZŽ Š  ‹ ®)D Œ D"°  z†{ Ž Š { Œ GH@Ž ŒZŠ G>@{6@A Š G Œ[ŒKŠ ­D{=F Š G  z†{





œ!% ž %



 




W



Š { ³B GH@ Œ z Š {C \pŒ ± DG"D Œ Š { ® ¯ ±D;G#B ®)DC F @{/° @{ °;±@CNDz Œ ± DGp@ @® zˆ°

  



9

: Q†F zjCpz†{ Š {lD Š F Œ ± D>C Œ @ Œ DC \ B¡+ 8# (N¤;¬ = 
#0W# ª ##¨#J,W+WK+eŒ ± D{Y{/Dz Œ ± DGR@{W@A Š



 )' (`'*P  $U28 b?f X G Š0Š F rk$*$n0# 5 $* (H#(%  N?j$*$*0^h'* L0(" (  ')("M

X

B  

%

= -
œ!%

¥O2R'* -  '*X|p0# 5 '*$*'UV2|?

B Q†FVy±@C;@|@A Š

w '*T')$)Zk0(" ª %

?j$*$)0^h(Z?†

 

Œ 1 +¡  N¤ z jD ° Š DCX{ ŠŒ Ž Š { Œ  @ zj{ ± D ±@C`@{6@A Š G Œ KŒ Š ­De { zjCz Fz Œ jz CNzj{ Œ ± > D C Œ@ Œ D

Š F Œ ± D`zj{ Œ GB°,DG

("  (

¨ %

8# (



(



6K œ!%*¨ % 7 Š G>@®j®gG"D"@Ž#±@A®)D < \ : †Q F VxzjCNzj{ Š {/D Š F Œ ± D>C Œ @ Œ DC \ B ¬ ± DG"D =
#0W# ª #%@bGDC Š ® B Œ z Š {ezjC Š { Œ ±D XE Ž#± @ {{lD ® @{6@A G Z ±@CT¯D ŒpŒKŠ @{C ¬ DG|@iGD B DC Œ>Š { Œ ± DIXpE Ž# ± @{ {/D ®f@{/° Œ ± D>G"D B DC Œ z†C Š { Œ ± D XE Ž#±@{ {lD ®

(



:

B W

(



W

(

(



W

W

W



”N("'* L=;5/;$*T! ^_;5 #'*

7. BALANCE

) :* K 'R #*K ž!% ª % NST3U4UV-*XWWYX)+b!2)+*XW3 ] :  W ± DG"DkzjCk@RGD"@Ž#± @A®)DTŽ Š {
³B!GH@ Œ z Š {  \ CBŽ#± Œ ±@ RŒ

Ž Š  ‹ ®)D Œ D° 

B G7



zj{



@{ °b± @C>@ @® zˆ°RŽ Š { Œ G"@Ž Œ








 

±@C

Š _ \/Œ ± DG"DhD
zjC Œ C G @®j®GD"@Ž#±@A®)DhŽ Š { ³B!G"@ Œ z Š { C GD"@Ž#± E \ zj{ Š ® 0zj{!³ Š { ® ¯ Œ  @A®)DmFG Š  ± D;G#B ®)DC Š F @{/° Y\ C BŽ#± Œ ±@ Œ Œ Š G ±@CbŽ Š  ‹ ®)D Œ D"°  zj{ @{ °X± @CRDz Œ ± DG B z p ±@C Š A Œ @zj{lD"°iDz Œ ± DGb@ @® zˆ°|Ž Š { Œ GH@Ž Œ;Š G=@{P@A Š G Œ ŒKŠ  ­ D{ F Š G  z†{



S

@®j®gG"D"@Ž#±@A®)D < \ : †Q FX§zjCzj{ Š {lD Š F Œ ± DXC Œ @ Œ DC \: B Œ ± D{I{/Dz Œ ± DG zj{ Œ GB°,DG

J

(

= # 65 = 3 

¬ ± DGD
 
#+-\ { Š Gp@=GDC Š ® B Œ z Š {IzjChzj{ Œ ± D 0zKD ¬\Š F Œ ± D

T+

1

B Q†FX ( B!z Œ CNF Š

F Š G  zjCZzj{ Œ ± D 0zKD ¬uŠ F Œ ± Dpzj{ Œ GB°,DG Š { ® ¯=z F -, ±@C`@TGDC Š ® B Œ z Š {bF Š G z†{







:

+ 

6K  ž!% œ!% 7 Š G>@®j®gG"D"@Ž#±@A®)D < : †Q F XS±@CI@{t@A Š G Œ ŒKŠ ­D{6F Š G



\

W

 tŒ  ± D{ ±@CI@{t@A Š G Œ  @{/°Tzj{i@®†®4Ž Š {  \ @ F Š G

³ B!G"@ Œ z Š { C "G D"@Ž#±@A®)D]FG Š  GDC Š ® B Œ z Š {F Š G  zjC`{ ŠŒ jz { Œ ± D 0zKD ¬xŠ F Œ ± D=zj{ Œ G#B°,DG=zj{






@RGDC Š

® B Œ z Š {TF Š G  dŒ ± D{XF Š G@®†®]C Œ @ Œ DC ±@ Dk@{e@A Š G Œ ŒKŠ ­D{


C Œ G Š



\fŒ ± D{

B Q†F@{R±



2

± Š {/DC Œ


@ @® zˆ°Ž Š { Œ GH@Ž Œ F Š G  zj{

A (  W





Š {/DC Œ B z Œ C Š GZ±@CN@{9@A Š Œ ± D{RF Š Gb@®†® \ GD"@Ž#± @A®)DNFG Š  Š  Š Œ Š Œ Œ ° DC;{ ±@ Dk@ @® zˆ°Ž { G"@Ž F







 


^[0 $U2X '*("  (H %



Z FY

S



cPO 0^d(H#hZ ("'*k?l5 -(" Jˆ?†("(m'*=-m?j$*'*("9% •Z0$*$   Y'*(]f')'U'‡$ v 'Uf(" _?/?& (%]„N("("-T_ _'* Nqa^[9. ')'*. $)( 

^h(".'* . -5 $*'*b 2e. 'U( W¡ ¤  ¡ ¤Lid("'*LtY,"# |^h'U !"# - $ ! e - ')¢!-p') ,'Uv  n  9k"- (H | 'U#

. "V2 `^h ("[.'* . - 5$*')] 2`. 'Um'*(f¡ ¤%qŸ[ '*(4 2

T5,2 `-(";?n$*`L #'*i-$* k% Np("- $U'* L v L-#')i5/ %Zr p- $U2("'*(/^_=("("- Tp  '*(   (Hb

'*(b(H"L$U2W '*("  (H0% w '* ')(= (H0]'U 095/`(" 0^h95,2R- ("'* LT'* -  '*X f?jp$*$4 v L- #'*( 0 5 $*Z?†  '*(_'*  $U2T Z?g Z(H#(  

 ['U?  'Uf (O '*0 RR5/" !'Uf ,([[L h $*') X,"# N R!')  JK ( % r ]_(H]?/[(" '*,5,2kN0 5 $*hv L-#')  ^[>T0i v L- #'*I0 5 $*>?† t^h'U-N >- (" ?4 $);L #'*X-$*% ™ p [("')p^[` =Z$*$*0^  >- ("k?]$*bL  #'*l^_b=("'‡  '* LR$*2eT("'* L$* '* (H# |?Z R., $h'*W'*("$‡'*\ Y Ti-" ! - T?4("  #$ ')(H#(%mcPZ 0Mq'U?h'),"-  ]# (_$U2 ;5/-  =!- =5/n?g(H. (, bp$*ZL #'*T-$) ([ - (" g  R p!- k5/ f?q"# (N'*(fv '*% ¥O2  ,^[Tb  L,(_ 5!2= Z.. $*'*0'* ?m-$* %

D 

; /, #/; / ;1 , #J;1 0 : - \

\

D

-

0 ; 2*, #%; 2  



B



D

 1  :,










6

J?KELNMGO:MQP*MQRO ƒ,%)% D Œ A#DX@IGD"@Ž#± @A®)D9Ž Š { ³B GH@ Œ z Š {\@{/° @CCB!D Œ ± @ ŒŒ ± Dbzj{ Œ GB°,DG Œ @­DCR@IA Š B!{ °,D"°e{ B!bADG Š F=C Œ D ‹ C Š GfD"@Ž#±  \l¬ Df°,D {/D[G"D"Ž B G#Cz D ® ¯>@ Š F]± Dz)³± Œ {z Œ D Œ GDD z \¬ ± Š C Dp{ Š °,DCN@GDp®*@A#D ®)D"°bA ¯=Ž Š { ³B GH@ Œ z Š {C;@{ ° ¬ ± Š C D;D"°0³,DC @G"D;®*@AD ®)D"°bA ¯>G#B®)DC Š F Œ ± D ‹ G ŠŒKŠ Ž Š ®4@{ ° Œ ± DNzj{ Œ GB°,DG Œ ± D Š G#zKDC ŒKŠ A#D Œ ± D Œ GDDŽ Š {CzjC Œ zj{!³ Š FN@;Czj{!³®)D[{ Š °,DZ®*@A#D ®)D° Z D {/D A ¯ Z S CCB!D Œ ± @ ŒN¬ Dk±@ DR°,D {/D° Œ ± D Œ GDD D Œ A#D Œ ±D C D ŒbŠ F|{ Š °,DC9@ Œ ± Dz)³± Œ zpzj{ zˆŽ#­8@8{ Š °D zj{ @{/° 9z Œ D Œ A#Db®*@A#D ®)D"°eA ¯ @{ °i®)D ŒhŒ ± Db{ Š °DC=zj{ Œ ±D ‹ @ Œ ± , 1 FG Š  Œ ±D>G Š0ŠŒfŒKŠ A#Dk®*@A#D ®)D"°X@C @{/° Œ ± DbD"°0³,DC Š GRD"@Ž#± zj{ Œ ± D ‹ @ Œ ±PADb®*@A#D ®)D"°I@C , 1 z†{ Œ ±@ ŒŠ GH°,DG Ž Š {  ³B!G"@ Œ z Š { @ {/°R@TGB ®)D :U °z DGD{ Œ FG Š  Z \ CBŽ#± Œ ± @ Œ ,     zjC|@Y°,DG#z @ Œ z Š { \ z F9@{¯ \ @°°Y@ Š Š Œ { °Db@Ck@9Ž#±!z&®*° F @A#D ® ±!zjC`{ Š °D @{/° Œ ± DTD"°0³,DfFG Š  ŒKŠeŒ ±!zjCT{ Š °D9@C XhD ‹ D@ Œ>Œ ±,zjC ‹ G Š Ž#DCCF Š GXD"@Ž#±Y{ Š °,D|zj{ zj{/Ž#D zjC { z Œ Dk@{ ° Œ ± D;{ B!TA#DG Š F Œ G"@ŽDC`zjC {z Œ D \OŒ ±,zjC ‹ G Š ŽDCC Œ DG#=zj{ @ Œ DC ",>ŒKŠ A#D Œ ± D;GDCB ® Œ zj{!³ Œ GDD D {/D zjCI°D {lD"° ŒKŠ A#D \ CBŽ#± Œ ± @ Œ




 =

7

: P


 



3&, \







3&, B

8 ]

3B, B  6 8< 3&,(B  9 . <
 6 . B .  #  #     B , #J, 6#E   , B  7
1 , 

      1  1  B 1    .  6 |$*') 6 ,"# 0%b„N$*("X("'* '*(; (H0 0  ; 0>5/e85/" e iR$*') e ,"# 0%>¥]2 ?&'U ("(n?jO(H 'U?  (OT5/" k\

0  B

W




 0Of$*'‡ `!"# 0%4c8]#n ] '* ^P  .("("0 ;'*€U0‚

(2 fk!"# h'*(fT.$* 0 R'U?mp. "V2./("(" ("("( 8$*') £,"# 0%“¡ˆ¥]2W?j'U  ("(N'U?p9 ')("(HR. "a2d ( 9$*') 8,"# >')8("TTv L-#')n 8'U?fb'*!"-   #(;$*26R5/-  0 i!- k5/ p?[(H.(4  6'*P$*$]=$*0?  ! (?n `,'*!- ')9" ` (Hp. "a2Xk- (HZ 0 =$*') X!"# ¤%    '*X-Z $U2 ("'*(f^[p^[- $) |(2 f p. ,$'* J (H#`'*(5/"0 9'U?  (Ni5/" I X'*(ZT.$* 0

'U?  (N=$*') 9,"#0%fŸ[ p?†$*$*0^h')LX  v 'U') (N`TJ '*0 |5,2RLTp(H"# L'*(%



X



6 [3B,  )1V? $&%   1. 

3B,

 

ƒ,% ª % S { D Œ A#D Œ ± D;Ž Š { Œ zj{ B@ Œ z Š { Œ GDD Š F zjCpC@z&° ŒKŠ AD>@ 
Tz Fpz Œ zjC;®*@A#D ®)D"°|A ¯ Œ ±D Œ ± D Š G#¯ Š F X Š GTA ¯i@9GB ®)D Š F Œ ± Dzj{ Œ GB°,DG Š GR@ zj{ °zˆŽ@ Œ DCX@eDCC@0³,DIA#Dzj{!³8G"D@°bFG Š  Œ ± D|{/D Œ&¬_Š G­ f‹ GD"°zˆŽ@ Œ D Š ŽŽ B!GCkzj{ Œ ± D ‹ G"D"ŽD"°,D{ Œ;Š F Œ ± DTG#B ®)D Z O \ Œ D ± D=D"°0³,D>z†CC@zˆ° ŒKŠ A#D 

J KELNMGO:M P*MGR'O

"D °0³,D Š F @9G#B ®)Dzj{ G#B ®)D Œ ±@ Œ UˆŒ ±@ Œ zjCk@ V Œ ± DG ¬ zjC

. B

@

_*9)+*  )+V?-$&%  






6

ƒ,% ¨ % D Œ A#DX@iG"D"@Ž#±@A®)D9Ž Š { ³B!G"@ Œ z Š {y@{ ° Œ N Œ Œ Œ Œ @C#CB!D  ± @ ± Dzj{ GB°,DG @0­DC@iA Š B { °,D"°i{B!TA#DG Š FbC Œ D ‹ C D Œ AD Œ ± DRŽ Š { Œ zj{B @ Œ z Š { Œ GDD Š F D Œ A#D|@9C D Œ;Š FbGD E Š   I  \ \4ŒKŠ A#D Œ ± D Œ GDD  @A®)D`D"°0³,DCZzj{ D {/D Š A Œ @zj{lD"°hFG Š  A ¯kGD Š 0zj{!³ Œ ± D;D"°0³,DCNzj{  @{/°T@®j® Š F Œ ± DzjG °DC Ž#D{ °@{ Œ C U zj{ Ž® B °zj{!³I°,DCŽ#D{/°@{ Œ COFB!G Œ ±DG=° Š¬ {-Z

Z

  Nz F Œ ± DGDkz†C>@{ CBŽ#± Œ ± @ ŒŒ ± D®)D"@HFb{ Š °,DC Š F   @GDT®*@A#D ®)D°eA ¯iŽ Š { ³B!G"@ Œ z Š { CTzj{ ¬ ±!z&Ž#H ± V\±@C;@{6@A Š G Œ_ŒKŠ ­D{ DkŽ@®j®   @{   Z

   Xz F Œ ±DGDz†CT@{ CBŽ#± Œ ±@ Œ=Œ ±Di®)D"@HFX{ Š °,DC Š F  @G"Di®*@AD ®)D"°WA ¯Y@dŽ Š { ³B E GH@ Œ z Š {C9zj{ ¬ ±!z&Ž#/ ± V…±@CI@ @® zˆ°YŽ Š { Œ GH@Ž Œ DIŽ#@®j®   @  J KELNMGO:M P*MGR'O

6 G3&,



3B,  P


3B,

3&,



 W"35 3 .

: 3  !2-W 3U!  E) \ 3 )  $)+&3

3&,

 O 3B,

3  !#-W 3U!  E) \ 3 ) )

B



)+* 3U T3 35 

8

  6

W

3&,




%'&3

@




 $)+&3 3U 

3&,

 O







\$-% +*9 YX)+

ƒ,% š% ± D ‹ G ŠŒKŠ Ž Š ®4zjCZC@zˆ° ŒKŠ AD 
z FhF Š G|@®j®nGD"@Ž#±@A®)D @{/°kF Š G|@®j®OA Š B!{/°C Š { Œ ± D \ Š Œ {B!TA#DG Š FC Œ D ‹ C Œ ±@ Œ @{Izj{ Œ GB°,DG;Ž#@{ Œ @0­D \ @ Œ ° Š DCp{   Š Œ Œ ‹  Š ¬ K Œ Š Š Œ Œ ‹  Š ¬ K Œ Š Š ‹ Œ ± @ D=A ± ± D DG @A G @{/° ± D DG Ž  ®)D D J KELNMGO:M P*MGR'O

!2)+*XW3



 !

W



™ f _?†_h., $/ O`5/h5 $)  0 g $)$^[Z 0

'*(ZR("0^  “ (N`./^_ Z|5/"p 9 T. $* ;?†  e5/- u\ I!- k5/ ?>(H.(R R I i'*,"-   - $) |#T¡j '),"-  h'*(h'*X$*'U')I^h'*X•p¤%

:

7.1 Balance for Honest O

c8p(H#pp?j$)$*0^h'* LT- ("'*`  v  'U'*gM



6




J KELNMGO:M P*MGR'O ƒ,% œ!% D Œ A#DX@iG"D"@Ž#±@A®)D9Ž Š { ³B!G"@ Œ z Š {y@{ ° @C#CB!D Œ ±@ ŒOŒ ± Dpzj{ Œ G#B°,DG Œ @­DC Š { ® ¯ { z Œ D ® ¯=T@{¯=C Œ D ‹ C D Œ Œ Š Œ Œ Š Œ Š Œ Š A#D ± D=Ž { zj{ B@ z { G"D#D F D A#Dk@T{ °,D`zj{ @{ °  @XC D ŒNŠ Fk{ Š °DC Œ ±@ Œ @G"DTŽ#±!z&®*°G"D{ Š F CBŽ#± Œ ±@ Œ @{¯iD"°0³,D A#D Œ&¬ DD{ @{/°R@TDTA#DG Š F z†C;@TGD Š @A®)DbD"°0³,D D {lD  ŒKŠ A#D Œ ±DC D Œ`Š FRŽ#±!z&®*°G"D{ Š F Œ ±@ Œ @GD9Dz Œ ±DGRz†{ Š G Ž Š {{lD"Ž Œ D"° ŒKŠ A ¯e@e{ Š { EˆGD Š @A®)DID"°0³,D zjC@{    
z F Z fz Œ ±DGkz Œ zjC;®*@A#D ®)D"°XA ¯|@XŽ Š { ³B!G"@ Œ z Š {Pzj{ ¬ ±!zˆŽ#± ±@Ck@{ @A Š G Œ[ŒKŠ ­D{ \fŠ G  zjC{ Š {lD ‹ Œ ¯|@{/°|D"@Ž#±9{ Š °,D Z ± DGD;zjC`@{ CBŽ#± Œ ±@ Œ z†{  zjCp@{6@A Š G Œ E ‹ Š¬ DGk{ Š °,D D`Ž#@{P°,D {lD   
TCzj=zj®*@G ® ¯

3B,

.

.

E) a(* ) E : 
B W

O

.


"g T5/  -("'*`  v '*'*X(f(" ("% rqO(Hn?  ](" '*k^[[("("- T  '*(nf0# 5 $*  v L- #'*g, f'*,"- ]#(]p5/- 0 =!- k5/ m?g(H.( 

P'*(Re ,'* - '*\" e? ^h'U\("./ RY '*( 5/-  g%4c8O 0]]?†$*$*0^h')Lp    '*>5/ V^_` ]./^_  b5/"N 95/""JK ! (%

.



3B,



43B,

6K 



 [

ƒ,%*%TSZŒ \ ± @C Œ ±D ‹ Š¬ DG  S ®C Š @ Œ zjC@{£@A Š G Œ E ‹ Š¬ DGX{ Š °D Ž Š  ‹ ®)D Œ D>z F Œ  ± D>G Š0ŠŒfŠ F jz Cp@|Ž Š { Œ G"@Ž Œ

3B,

3&,



ŒKŠ @A Š G Œ z F Œ Š ŠŒ_Š F ± DG 0 ‹ Š¬ D G ŒKŠ ±@C Œ ± D E ‹ Š¬ DG={ Š , ° D

 Z\



9

F3&,

G Š0Š F ¥]2i') - '*ei ='*L,;?f ! k'*ek" ! ^[I("0^s 'U?`  § (T X./0^_ Y5/"T u$*$  k ! (p'*885/""Jˆ"=T5/""JK./0^[ `! (%kr p   N 'U '* ^[;(" 0^  0^t=# ,(">k(" Z?q0 L(h') ! '* -  '*$U2R("- #|   '*(ZI5/""JK./0^[ h"%

 Z

3&, Z3B, "# R%$ER'&&MQP*MQRO ƒ!% ª % O D± @WD : Z Q†F=@{ Š °,D .\ zj{ 3B, zjC`®*@A#D ®)D"°9A ¯9@XŽ Š {
³B!GH@ Œ z Š {Pz†{ ¬ ±!zˆŽ#± ± @C`@{6@A Š G Œ ŒKŠ ­D{ Œ ± D{iz Œ zjCN{ ŠŒ @|Ž Š { Œ G"@Ž Œ E ‹ Š¬ DGb{ Š °,D B Z Q†F=@{ Š °,D .\ zj{ 3B, zjC`®*@A#D ®)D"°9A ¯9@XŽ Š {
³B!GH@ Œ z Š {Pz†{ ¬ ±!zˆŽ#± ± @C`@ @® zˆ°Ž Š { Œ GH@Ž ŒfŒ ± D{ez Œ z†Cp{ ŠŒ @{6@A Š G Œ E ‹ Š¬ DG>{ Š °,D F Z < B ‹‹ Š C D Œ ±DGD>zjC@Ž Š {
³B GH@ Œ z Š {   \ CBŽ#± Œ ±@ Œ D DG#¯T{ Š °D zj{ 3&, ®*@A#D ®)D"°PA ¯  zjC{ ŠŒ @{\@A Š G Œ E ‹ Š¬ DG9{ Š °,D Q†F . zjCR@ , \ C#BŽ#± Œ ±@ Œ z Œ zjC;®*@A#D ®)D"°XA ¯  — @{/°  —   A ¯R@{ { Š °D>zj{ 3&< @ ‹‹ ® zˆŽ@ Œ z Š { Š F=@GB ®)D Œ ±@ Œ ®*@A#D ® C>@|{ Š { EˆGD Š   @A®)DD"°0³,D \fŒ ± D{ . zjC{ ŠŒ @{e@A Š G Œ E ‹ Š¬ DG={ Š °D R Z < B ‹‹ Š C D Œ ±DGD>zjC@Ž Š {
³B GH@ Œ z Š {   \ CBŽ#± Œ ±@ Œ D  DG#¯T{ Š °D zj{ 3B, ®*@AD ®)D"°iA ¯  z†C>{ ŠŒ @IŽ Š { Œ G"@Ž Œ E ‹ Š¬ DGR{ Š °,D Q†F . z†C=@ , \ C#BŽ#± Œ ±@ Œ z Œ zjC;®*@A#D ®)D"°XA ¯  — @{/°  —    A ¯R@{ { Š °D>zj{ 3&< @ ‹‹ ® zˆŽ@ Œ z Š { Š F=@GB ®)D Œ ±@ Œ ®*@A#D ® C>@|{ Š { EˆGD Š   @A®)DD"°0³,D \fŒ ± D{ . zjC{ ŠŒ @Ž Š { Œ GH@Ž Œ E ‹ Š¬ DG={ Š °,D "# R%$ER'&&MQP*MQRO ƒ!% ¨ %6 D Œ < A#Df@GD"@Ž#± @A®)DZŽ Š {
³B!G"@ Œ z Š { \ @{/° Œ G Œ ± DTŽ Š { Œ zj{B @ Œ z Š { Œ G"D#D Š F <  6 D Œ A#Db@{ Š °,D=zj{ Œ G \ ®*@A#D ®)D° < \ V zjCTz†{u@ A ¯6@8Ž Š {
³B!G"@ Œ z Š { <  < B ‹‹ Š C DpFB!G Œ ± DG Œ ± @ Œ zj{  W C Œ @ Œ Diz†{ ¬ ±!zˆŽ#±£z Œ ±@C|GD ( B DC Œ D"°|F Š GI@{ @A Š G Œ ŒKŠ ­D{8F#G Š  @{ °Tz†C ¬ @z Œ zj{,³ZF Š G`@bGD ‹ ® ¯ \ @{/° W ±@C;@{ C ¬ DGD"°X@bGD ( B DC ŒhŠ { Œ ± DIVfE W Ž#± @{ {/D ®  W ± D{eDz Œ ±DG  zjCh{ ŠŒ @{i@A Š G Œ E ‹ Š¬ DG`{ Š °D Š G  zjCN{ ŠŒ @|Ž Š { Œ G"@Ž Œ E ‹ Š¬ DG={ Š °,D 9 G Š0Š F M=¥O2P$*TXœ!% šn'*    '* =d5/" P'*(>   (. ‘   $4;b( I'*(9 (    $&% ‰ ?  p5/"  |'*(fR  (  #    $   00 R'U 5,2 p-(";?q-$) V  7 %2 X   ;5,2../("'U'*eƒ,% ª  . '*(Z  |5/""JK./^_ h ! % w '*T'*$)$U2, 'U?m;("$*-'*X?† t  '*(f   (    $& ^[; 0M ')(hZ95/""JK./0^[Zg% "# R%$ER'&&MQP*MQRO ƒ!% š%6 D Œ < A#Df@GD"@Ž#± @A®)DZŽ Š {
³B!G"@ Œ z Š { \ @{/° Œ G Œ ± DTŽ Š { Œ zj{B @ Œ z Š { Œ G"D#D Š F <  6 D Œ A#Db@{ Š °,D=zj{ Œ G \ ®*@A#D ®)D° <   < B ‹‹ Š C DhF#B G Œ ± DG Œ ± @ Œ zj{ <  \ VzjC`zj{P@ A ¯I@XŽ Š {
³B!GH@ Œ z Š {  ŒC @ Œ DZzj{ ¬ ±,zˆŽ#±bz Œ ± @C[GD ( B DC Œ D"°[F Š Gh@{R@A Š G Œ ŒKŠ ­D{F#G Š  W @{/° zjC ¬ @z Œ zj{!³hF Š Gp@bGD ‹ ® ¯ \ @{/° W ±@Cp¯D Œ_ŒKŠ @{C ¬ DG>@bGD ( B DC ŒhŠ { Œ ± DIVfE W Ž#± @{ {/D ®  W ± D{eDz Œ ±DG  zjCh{ ŠŒ @{i@A Š G Œ E ‹ Š¬ DG`{ Š °D Š G  zjCN{ ŠŒ @|Ž Š { Œ G"@Ž Œ E ‹ Š¬ DG={ Š °,D 9 G Š0Š F M|¥O2Y$*T9œ!% š8'*  ]X5/"k0¢,- (H=')(=Y  (  ‘   $&% w '*   (k2, T (H^[0 £i0¢,- (H |  ($   $g'*  '*N0I(H^[ N'U |p^h $) v L-#')I^[-$) 9L'*!Rbv L-#'*  —l'*9^h '*#   (T(H^[  uI0¢,- (H=d  ( «    $f5,2P |- (" ?Ok?O;- $*(p'* `  %pŸ[k. ./("'U'*e 0^x?j$*$*0^h(;?† ../("'U'*eƒ,% ª  R..9ƒ!% ¨ %

6K




Ž Š { zj{ ¬ FG Š  @A Š G

9

6 

ƒ!% œ,% D Œ A#DR@9{ Š °DTzj{ Œ G ¬ ±,zˆŽ#±ezjCk®*@A#D ®)D°iA ¯i@ Œ Š  ‹ ‹ Š \ VzjCpz†{8@C Œ @ Œ D ³B!G"@ z { B CD[F#B G Œ ± DG Œ ±@ Œ z†{ ±!zˆŽ#±Iz Œ ±@C`GD B DC Œ D"°>F Š Gk@{Y@A Š G Œ ŒKŠ ­D{ Š Gb@GDC Š ® B Œ z Š { @{/°9zjC ¬ @z Œ zj{!³`F Š Gb@9GD ‹ ® ¯ \NŒ ±D{\Dz Œ ± DG zjCk{ ŠŒ @{ Œ E ‹ Š¬ DGk{ Š °,D Š G  Š Œ Š Œ Œ ‹  Š ¬ Š zjC{ @|Ž { G"@Ž E DG={ °,D

W

0T(H# ('* % w = N?j$*$*0^h'* LR0("(Z')("M % ª %



  ¡+ 8# (N¤    M]¥O2X$*Tkƒ!% œ,% , ¡+ 8#N( ¤    M 0X0¢,- (HN95/" X?‡  5,2b Z- ("N?- $* V    TL>=`(H# w — ("-T    ¡+ 8# N( ¤   —%WŸ[ |("- $Ub?†$*$*^h(5,2Y0("8X

../("'U'*eƒ,% ª %

¨!%

š % œ,%

\ 8#(   

 + 8#(  

7

, 5,2Rp- ("p-$* V +¡  N¤ M 09("

 L `>>(H# w —!   ("- #b  ,¡+ N¤ — %]Ÿ[ h("- $U ?j$*$)0^h(N5!2R0(" ª    X../("'U'*eƒ,% ª %



8#(   



C T+



ƒ,%

  ,¡+ 8# (N¤   



!%

1 , , ¡+ 8#(N¤     1 ,
1¡+ 8#(N¤    
/  ¡+ 8# ( ¤   M  (Z=$*') |,"# N R("- $Uf?†$*$*^h( N

) *:K 'R #*K

QW

6







7.2 Balance for Honest R

c8> '*("- ("(5'* © 2X5 $‡ >?jp  (H:k

%„N("("- Tp ') DN4V^[X.'* '*. $*(  . …^h ("T. '*-.- 5 $*'*T 2i. 'U( £¡; /, #%; / ¤ x¡;1 , #%;1¤NLed("'*L P,"# |^h'*  ,"# - $g !* e - ')¢,- p') ,'*v  Mm  9="-(H0 R'*#

. "a24`  h^h ("e.'*- . -5 $*'*e 2u. 'U9'*(6¡; 2*, #%; 2 ¤% Ÿ[ '*(  2y d5!2£ i- ("e?`$)6L #'*t-$* k  % |

3&,

3&,

3&,  P


3B,



)+*93U T3 3U 

 W3U 3 .

3B,





8

  6

 O

%'&3

3&,

QW






 $)+&3 3U  3  !#?W 3U!  E) a>3 )L)

B

D








6

(

&

.

*9)1*  )+V? $&%' 

: 3  !#-W 35!  E) a 3 )  $)+&3

± D ‹ G ŠŒKŠ Ž Š 4 ® z†C;A@®*@{ ŽD"°NF Š G± Š {/DC Œ V

Ÿ[I5/X  v  'U'*( d.,?j(?5 $‡ X0£5/9 !J    Ik- $U'*. $*>- (N?] >., $&%>Ÿ[  => `?j$UJ $*0^h'* LT'*T./"#,Z '*(H'*  '*(N'*R ;  v '*'*M 0¤ ‰ (H0 `? '),'U')$ (" m? ?& ( N^[[(H#"m^h'U=b5'U#"2 # 5$*> v L- #'*g% ª ¤Nr >  (H"- '*i?Obv 'U> ,'* - '*I"l$*LJ ^h'UY R!- k5/ >?N(H. (> > R'*,"- =(H.(n^[|$*(" .-k95/- 6T!- =5/`?h'*T(; b$*RL #'*d-$* 95/;-("0 g% ¨¤f~OI0 L;?q ;,')!- '*X" ;')(h^x$)5/$*0 |5!2 -$*;5/'* L=-("0 X$* L^h'UX p 2?qp.'*'*. $l'*!$* g% š¤;„N,2i0 Lb `')(>$)5/$*0 65!2 k} (;26kX 2i! 0^h8 ;'*!"-  [')(N$*("k T5$*p0 L% œ¤]Ÿ[h., $ '*(](') =;5/h5 $) 0 =?†O  (H ,'U?/?jf$*$ # 5$*kv L-#'* ( / |?†$*$q5/- (ZX ;!-bJ 5/_?(H . (n nf'),"-  n#(_ =f -=5/ n?/'*T( $*pL #'*X-$*p'*(f- ("0 l   x ,(fh 5/ ;./0^[ hT5/"N R ./^_ Z=T. $* %

. B

ƒ,% ƒ,% D Œ A#DX@IGD"@Ž#± @A®)D9Ž Š { ³B GH@ Œ z Š {\@{/° Œ  Œ Œ Œ Œ @CCB!D ± @ ± Dbzj{ GB°,DG @­DCR@IA Š B!{ °,D"°e{ B!bADG Š F=C Œ D ‹ C D Œ A#D Œ ± D|Ž Š { Œ zj{ B@ Œ z Š { Œ G"DD Š F D Œ  A#DR@IC D ŒpŠ F=GD E \qŒKŠ A#D Œ ± D Œ GDD  Š @A®)D`D°³,DCNzj{ D {/D I\ Š A Œ @z†{lD"°fFG Š  Š Œ  A ¯>GD 0zj{!³ ± D`D"°0³,DCz†{ @{ °T@®j® Š F Œ ± DzjG °,DCŽ#D{/°@{ Œ C U zj{/Ž® B°zj{,³I°,DCŽD{ °@{ Œ C_F#B G Œ ± DGk° Š¬ {(Z

Z

  Nz F Œ ±DGD=zjC`@{ CB Ž#± Œ ±@ ŒNŒ ± DR®)D"@HF={ Š °,DC Š F  @G"DR®*@A#D ®)D"°iA ¯eŽ Š { ³B GH@ Œ z Š {CTzj{ ¬ ±!zˆŽ#±RDz Œ ± D G Xy± @C B z ŒnŠ Gf±@CN@{X@A Š G ŒnŒKŠ ­D{ DŽ@®j®  @{ 

Z

   9z F Œ ± DG"DzjCb@{ CBŽ#± Œ ±@ ŒkŒ ± Di®)D"@HFX{ Š °,DC Š F   @GDI®*@A#D ®)D"°dA ¯d@dŽ Š { ³B E G"@ Œ z Š { CXzj{ ¬ ±!zˆŽ#± ±@CI@ @® zˆ°YŽ Š { Œ G"@Ž Œ DIŽ@®j®  @ 

../("'U')iƒ!% ª % ƒ,% !%

 

 )+V?-$&%   1. 



J?KELNMGO:MQP*MQRO

   M  (Z 1 ¡+ N¤ 5/" `  q("-$U4?j$*$)0^h(4?‡  . ./("'U'*=ƒ!% ª %

?†

6 [3&,

.X

ƒ,% ž!% S { D Œ A#D Œ ± D;Ž Š { Œ zj{B@ Œ z Š { Œ G"DD Š F zjCpC@zˆ° ŒKŠ A#Dk@ 
Tz Fpz Œ zjCp®*@A#D ®)D°RA ¯ Œ ± D Œ ± D Š G#¯ Š F Š GA ¯i@9GB ®)D Š F Œ ± Dbzj{ Œ G#B°,DG Š G@ zj{/°z&Ž#@ Œ DCX@eDCC@0³,DIADz†{!³6GD"@°TF#G Š  Œ ± DX{lD Œ&¬OŠ G"­ ‹ G"D"°zˆŽ@ Œ D Š Ž#Ž B!G#C=zj{ Œ ± D ‹ GD"Ž#D"°,D{ ŒpŠ F Œ ± D=G#B ®)D Z O \ Œ D ±DbD"°0³,D`zjCC @zˆ° ŒKŠ A#D 

J?KELNMGO:MQP*MQRO

3&,

C

 >



"D °0³,D Š F @9GB ®)Dbzj{ G#B®)D Œ ± @ Œ UˆŒ ±@ Œ zjCk@ V Œ ± DG ¬ zjC

$








8#(   



Z



>

8# ( 



N

1+¡  N¤ M 0R("

1h5,2bN-("N?4- $* V   IL|T(H#  —g("- #9  2¡+ N¤ —%`Ÿ[ ("-$*h?†$*$*^h(N5,2|(">œ= X. ./("'U'*eƒ,% ª %





D

1 ,  ¡+ 8# (N¤    M]¥O2|$*T=ƒ,% œ!% 2¡+ 8#N( ¤    M 0X0¢,- (HZ>("$*-'*9?†  5,2  =- ("b?[- $* V 5 *I   6LXIR(H#  —4("- #6  1 ,  ¡+ 8# N( ¤ H —%iŸ[ ("- $Uk?†$*$*0^h(b5,280("ši

../("'U'*eƒ,% ª %

ž!%



\

("-$*'*LXv L-#')65/ %>r ;-` $*2 ("'*(g^[b("("- T   '*(;  (H>

'*(;(H"L$U26 '*("  (H0%=r  k (H ?hT(" '*gO5,28X0# 5 $*R v L- #'* m^_RTY v L-#')60 5$)k?† x^h'U - p k- ("k?_k$) L   #')9- $*% ¥_- ("N? l '*  ("(]?j[ (H >!$*$  Z$*0? ! (['*  ; ,'* - '*|";^[-$) 95/;$‡5/$*0 95,2R v L- #'*('* ^h '*# Y (g'U m¢,- 'Ug4 (g5 #'*  p'U  q 5/"   XP$*') u,"# 0%’„N(5/ ?†h^_e(2£ I., $  (;("-  ("(H?j-$)$U26T.$* 0 I'U?[ k (H;. "V2 5 #'* (` $*') P,"#T Y5/"0 P'U? s'U b¢,-'*(>=5 #'* (= 5/" % n$)("i i 0hY '*(" (H \5#'* 5/dI$*') Y,"#b dd5/" g%8Ÿ['*(='Ub0W  5,2kv(H]    L'* L;("'*L - (O^h'U \5,2=-("')Lp h  # L .,$h 8P0¢,- (H'*L ?jTW5/" g% N0^fJ 0 5,2T?&'U ("(Z("'*  ^h'*$*$4$U^f2 (N5#'*Ik$)') R,"# 'U? 5 #'* (`R$*'‡ e,"# 0 08$U^f2 (`$)'*  ;  !"# Z'*(Z$*') g%




3B,

3B,

 O







\$?%'+* " YX)+

ƒ,% !% ± D ‹ G ŠŒKŠ Ž Š ®gzjCC@z&° ŒKŠ A#D 
z FNF Š GR@®j®]GD"@Ž#±@A®)D @{/°=F Š G|@®j®[A Š B!{ °C Š { Œ  ± D \ Š Œ { B!bADG Š FC Œ D ‹ C Œ ±@ Œ @{Izj{ Œ GB°,DG`Ž@{ Œ @0­D \ @ Œ ° Š DCp{   Š Œ Œ ‹  Š ¬ K Œ Š Š Œ Œ ‹  Š ¬ K Œ Š Š ‹ Œ ±@ DkA ± ± D DG @A G @{ ° ±D DG Ž  ®)D D J?KELNMGO:MQP*MQRO

!#)+*9XW"3

W





6

ƒ,% ›!%








J?KELNMGO:MQP*MQRO D Œ A#DX@IGD"@Ž#± @A®)D9Ž Š { ³B GH@ Œ z Š {\@{/° Œ _ Œ Œ Œ Œ @CCB!D ±@ ±D;zj{ GB°,DG @­DC Š { ® ¯ {z Œ D ® ¯=b@{ ¯=C Œ D ‹ C D Œ A#D Œ ± D=Ž Š { Œ z†{ B@ Œ z Š { Œ GDD Š F D Œ A#D=@{ Š °,D>zj{ @{/°  @XCD ŒNŠ F>{ Š °,DC Œ ±@ Œ @GDTŽ#±!zj®*°GD{ Š F CBŽ#± Œ ±@ Œ @{ ¯9D"°0³,D & Œ ¬ Š Š A#D D#D{ @{/°R@TDTA#DG F zjC;@G"D @A®)D=D°³,D D {/D  ŒKŠ A#D Œ ± DCD Œ;Š F|Ž#±,z&®*°GD{ Š F Œ ±@ Œ @G"DXDz Œ ± DGzj{ Š G Ž Š { {/D"Ž Œ D° ŒKŠ A ¯6@i{ Š { EKG"D Š @A®)DID"°0³,D z†C@{    
bz F Z fz Œ ±DGbz Œ zjC=®*@AD ®)D"°iA ¯i@iŽ Š { ³B!G"@ Œ z Š {£zj{ ¬ ±,zˆŽ#±PDz Œ ± DG ±@C B z ŒfŠ G±@C`@{6@A Š G Œ[ŒKŠ ­D{ \[Š G  zjCn{ Š {/D ‹ Œ ¯p@{/°`D"@Ž#±>{ Š °,D_zj{ Z ± DGD_zjCO@{ CBŽ#± Œ ±@ Œ  z†Ch@{X@A Š G Œ E ‹ Š¬ DG{ Š °,D DNŽ@{X°,D {/D   
TCzj=zj®*@G ® ¯

3&,

.

.


D z F Œ ± D>G Š0ŠŒfŠ F jz C;@RŽ Š { Œ GH@Ž Œ E ‹ 

3&,

J 6 3B,  P


 Z

Š ŠŒOŠ F zF Œ ± DG 0 Œ ‹  Š ¬ ± D D G ŒKŠ Š °D





"# R'$ R'&&M P*MGR'O : ZQ†Fk@|{ Š °D .\

O

W

ƒ!%* % Dp±@ D jz { zjC`®*@A#D ®)D"°9A ¯X@9Ž Š { ³B!G"@ Œ z Š {Yzj{ ¬ ±!z&Ž#± Dz Œ ± DG  Š Gm±@C_@{@A Š G Œ ŒKŠ ­D{ Œ ± D{Tz Œ zjCn{ ŠŒ @;Ž Š { Œ G"@Ž Œ E ‹ Š¬ DG { Š °,D Z †Fk@|{ Š °D \ zj{ zjC`®*@A#D ®)D"°9A ¯X@9Ž Š { ³B!G"@ Œ z Š {Yzj{ ¬ ±!z&Ž#± Š Œ f Œ ±@C>@ @® zˆ°|Ž { G"@Ž Œ ±D{ez Œ zjCN{ ŠŒ @{6@A Š G Œ E ‹ Š¬ DG>{ Š °,D \ C#BŽ#± Œ ±@ Œ D DG¯T{ Š °,D Z B ‹‹ Š CD Œ ± DGD;zjCp@Ž Š { ³B!G"@ Œ z Š {  Š Œ Š Œ ‹  Š z†{ ®*@A#D ®)D"°PA ¯ zjCT{ @{y@A G E ¬ DGI{ Š °,D †F zjC|@ — @{ ° —  { Š °,D>zj{ E\ CBŽ#± Œ ±@ Œ z Œ zjC;®*@AD ®)D"°|A ¯ A ¯|@{ @ ‹‹ ® zˆŽ@ Œ z Š { Š Fk@|GB ®)D Œ ± @ Œ ®*@A#D ® C=@{ Š { EKG"D Š @A®)DRD"°0³,D \fŒ ±D{ zjCp{ ŠŒ @{8@A Š G Œ E ‹ Š¬ DGk{ Š °,D \ C#BŽ#± Œ ±@ Œ D DG¯T{ Š °,D Z B ‹‹ Š CD Œ ± DGD;zjCp@Ž Š { ³B!G"@ Œ z Š { z†{ ®*@A#D ®)D"°eA ¯ zjC>{ ŠŒ @IŽ Š { Œ GH@Ž Œ E ‹ Š¬ DG|{ Š °,D †F zjC=@ — @{ ° —  { Š °,D>zj{ E\ CBŽ#± Œ ±@ Œ z Œ zjC;®*@AD ®)D"°|A ¯ A ¯|@{ @ ‹‹ ® zˆŽ@ Œ z Š { Š Fk@|GB ®)D Œ ± @ Œ ®*@A#D ® C=@{ Š { EKG"D Š @A®)DRD"°0³,D \fŒ ±D{ zjCp{ ŠŒ @Ž Š { Œ G"@Ž Œ E ‹ Š¬ DGb{ Š °D







B Q

3&,

R
O("-$*m`?j$*$*0^h(O?‡ 0("h¨ k. ./("'*'* ƒ!%* %

0   ¡+ 8#   M]¥O2. ./("'U'*9ƒ!%*0k•y')(fh`!"# 

ž!%

./0^[ Z! %

0 1 ,¡+ 8# (N¤    
/ 

ƒ,%

8# (    

+¡  N¤ M … (`X$*'‡

!"# N R p ("- $Uh?j$*$*0^h(N?‡s../("'U'*eƒ,%) %

0

!%

8#(    2

1*3


/  8# ( 

T+

2 +¡  N¤ M ("

4h5,2=Z-("N?Z-$*  =- ("T?_- $* X  6LXIR(H# —q("- #6  +¡  N¤ — %6Ÿ[ T("- $U>?j$)$*0^h(T5,28("Xƒ9

../("'U'*eƒ,%) %

QW

) *:K 'R #*K

ƒ,%)¨ %





± D ‹ G ŠŒKŠ Ž Š 4 ® zjC`A@®*@{ Ž#D°NF Š GN± Š {lDC Œ X

˜ L'*Y   v ,'*Y 8. ,?Z0P5/ ! 0 e?†    -",h- (% „Z$U -Lp^__ f q '*("-("(4'U4 5 $)  ]?†q(H ') (" \'*(O  (HOn^[0 $U2b '*("  (H0 k5 $) f?j_(H '*£0(" '*(R(H0[^[!$U2\ ')("(HR0\5/X("')T'*$)$U2 (H#0 9 |. 0 g%



M





=

=


(  U = A# U8# 9< 3 #  (

M  U = 3/# U7# #





[

EY

03&,

5/`$‡5/$*0

% w '*  '*(=0 5$)>J G Š0Š F M  v L- #'*g4^[T 0 k- (H;5/=')6T?f'U(`X(H#(`') % w = N?j$*$*0^h'* LR0("(Z')("M



8



- ('* '*0I 0^S(H"#L'*(  bf ("')   u'*u  .  '*- (e(" '*“2 5/P?&'* ?j-$)$U2  .(",0 (i?j$

')'* (f'*|$*'* Z$*L'*T€U‚ˆ  ! '* L` Z. (",#'* ?O7 w • "#(h ("')   X'* € ¨‚ˆ% „…‹ B!GD `Š G#{u@ z Š  '*(b  v 0 P(M P¡ ¤ 
¡ ; ¤% „N,2?n'*(hL-  |'* (H#  (N?q ?†9M P¡ ¤ 
¡ ;¤ '*(;  ')0 e?h(` zj{C Œ GBŽ Œ z Š { "#(H?j Pv L-#')\?;9?j9M  P¡  ¤  ['*, ¤  ^h  |'*(h   ; v L- #'*gM  ¡ ; Z?q?‡("  (H#!(% „  v L-#'*x?bY(H2 (H '*(X .(",0 t(IP (" ?fv  'U$U2e,2eT'*b?jk- $)(%|Ÿ[T0("T^h $*$_./(HJ ("'*5 $*e '* (R?`8(H2 (H ("-$‡ £5/9#£'*!P- ,R'*(

 (" '*5/0 i^h'Ui k $*.i? A G"@{ Ž#±!zj{!³ ;Š G#{F Š G#=B ®*@C ?O  ?j 
p¡ ,  1   p¤%XŸ[  Gzj{,³ ?h("- #YP'* J (H"- ')I("- $U(p'*9 ># L>?]  – (H#— 'U  ;'*,   – (H# — ,]R'*!e  – (H# — 1 OI%%0%_R'*!e  % ¥_-h^_k b !^ zj{6@° @{/Ž#D ^h'*9?m (" – (H#— $* '* (k^h'*$*$[5/T("db9L'*P,("'* €U ª f¨‚ˆ% Ÿ[ Y("P^h d$*$k./("("'*5 $*W '*( 1 )% %% ²(" - $) 5/ #9'*,- ,0 ^h'UI.!') '* LT-N0^hI'*>5/ V^_ , ,0*%%%  , b^h'*$*$m5/> ("')5/ i5,2|T0(N?O ;Š G#{ EK® z‡­D[F Š GE 
¡"¡ , , ,  ¤  1  ¤% =B ®*@ ?m ?†

ƒ,%* ª % D Œ #A DX@I{ Š  ° Dzj{ ± D{\Dz Œ ± DG zjC { ŠŒ @{I@A Š G Œ E ‹ Š¬ D G>{ Š , ° D Š G z†CZ{ ŠŒ @TŽ Š { Œ HG @Ž Œ E ‹ Š¬ D G`{ Š °,D

.

R

8. REPRESENTATION IN LINEAR LOGIC



3&,  W



*






  Q .  

ƒ,%*% 6K D Œ A#D=@{ Š °,D`z†{ Œ G ¬ ±!zˆŽ#±XzjC;®*@AD ®)D"°RA ¯|@ \ Xuz†COzj{T@C Œ @ Œ Dfzj{ Ž Š { ³B!G"@ Œ z Š { B ‹‹ Š C DF#B G Œ ± DG Œ ± @ Œ z†{ ¬ ±!z&Ž#±Tz Œ ± @CfGD B DC Œ D°hF Š GZ@>GDC Š ® B Œ z Š {;FG Š  @{/°`zjC ¬ @z Œ zj{,³ ŠF GT@XG"D ‹ ® ¯ \hŒ ± D{£Dz Œ ± DG  Š Œ Š Œ ‹  Š ¬ zjCk{ @{d@A G E DGR{ Š °,D Š G z†Cp{ ŠŒ @|Ž Š { Œ G"@Ž Œ E ‹ Š¬ DG={ Š °,D






L2



]

* &

%8#




% %8#



M

%8#

] < ( =  B /< ( = *  8< ( =  M =  = B =  =

< (

 W

$% 

;

%

* %8# &  = #





cPT   e Ž Š  ‹ G"D± D{ Cz D  T. - #'* $]'*!. #J '*X?† 9$*'* 0N$*L'*`'),"! - 0 |')6€U ª 0¨‚K%

MX

)*'KER'#*K !"$#

%'&P

M

# ¡ ; , ; ¤

2

 R- (. . $U2W '*(R..£8 9("i?pI.!'*-( ("  '*i^h  kT(H" L$U2i '*("  (H. "') '). , '*(.$)02 '* L L')(H|9L- . ? –   ("— f^h '*#u ("'*(H(?  `% 1 *%0%% P'*(IY$*'*(H9?k$)$ >} (R- $*( ; w - ../("i  [,0 '*,"-  _-$*(  R$*$l-$*(_'*T^h '*# q. 0 '*0([,- f =$*'*(H n i=$*'*(H :1 2 *%0%% '* $*- (;$)$n >- $*(;? ;../  !([?‡ k% ¥O0-("?h(". T (H"#'*,(q^_R(" e b'*P./'*,( ?g-O$*'* 0_$*L'*! '* L %qcPZ (" '*5/f f0("N?4p("'*L$* -R^h'U|R  (H  R`(H" L$U2X '*(" (H k%]Ÿ[0(" ?p9("'*L$*|-P^h'*WY (H  8^[0 $U2P '*("  (H 95/;("'*T'*$)$U29 (" '*5/0 l% „Z- '*$*'‡"2 Ž Š { Œ G Š ® @G#zˆ@A®)DC M
!
, , *%%%0
, 
$1*%0%% 
  '*,"! -0 l%XcPb?† u'*P b?†$*$*0^h')Le^[2,%9~]#Y?f 5/ ?m N?j ¡ 
¤_'*( – L- # 0 —(MZ¡"¡
,  i¤ k5/0 
,¡
/ ¤"¤%m~]# _?! m?j ¡ 
¤ '*( – L- # 0 — (MX¡"¡
 ¤ 
p¡
 ¤"¤#%X„N e^[R 6b?j$*$*0^h'* Le!J '*9M

¡"¡
9, ,
,  ¤ 
1  
;¤% ‰ P 'U') ^_| 0Te'*,"! -RI -=5/ `? d ')T(>i  $* =0("(p^h = "#'*8 5 $*'* LR 'U'*(`k '*$‡0 £¡ˆ ("'*T'*$)R("'U- ')£^h'U£9., $n !J  -'*d"]^h '*#W^_|d.0 P?jT- T ("'*£?N ., $h5,2Y'* - '*T  ! (% ˜ -=.,?$*'*(T 1 37 i(H"Li '*£?Z?j'U  ("( .0 P?‡ €U‚ˆO^h'*d'U("$U? ^_k?†$*$U2I(H#0 e'*I >=-$U')(""JK^f'*'*L?†$)'*(" 

. 0 £5,2d'* -  '*|T  ! (%uc89 0X$*("Y(" 0^[ W  R ("'*6?h5 -(" Jˆ?†("(`2I5/=. (",0 i')e T(p? . 5 '*$*'*a2I'*8$*L')$](H2(H 9/'*e^h')#I?j$n ')'* (  "("./ |=?†- $*$4 -'*R"(Z X!'*p (!% ˜  b./("("'*5 $*X?jT(b?p5- (" Jˆ?†  ("(k'*d65/R'*J (H'*L g% ˜  f  ("'*#5 $*. ./ "'*(_?l  1 3,7§. ,$ˆ ("->(4 Jˆ.- ')')> ]"-(H0  'U# ;. "V2p- ,"J 5 '*$*'UV2,O(H')$*$['*de5/X'*!(H'*L0 d(k^[$*$&%WŸ[ |$‡" 

^h'*$*$4'*!$*Z?j$*')< ')LT./,')$*$U2| '*("  (HhZ0$*("(NJ '*(?] ;"-(H0 X 'U# 9. "V2,%hcP>$)("R. $)i. .$*29- # '‡¢,-(Z $U2 % w 0 !/%!„tT #Ja#')R?†h. ,$ $*2 ("'*(% ]Š  ‹ B Œ DG ‰  G Š Ž E Œ ± S {{ B@® D"Ž B!Gz Œ ¯ Š B!{/°@ Œ z Š { C XŠ G"­CH± Š‹  . L(œœ ,ž›! 7X#    ‰ #$U2gg0›››!% ‰ ~]~]~ ‘ T.-  w ,'* V2 m("(% € š‚ k% ‘ "'* 0l3 %/7X'*$*$*  k%•N-("(% n!'* Lb(" 2|')( 0(H2| - L% ‰  ]Š  ‹ B Œ DG E Œ ± S { {B @® Š B { °@ Œ z Š { C XŠ G­CH± Š#‹  . L(N›ƒ 0  D"Ž B!Gz Œ ¯ ª !% € œ0‚ w % o (h o % o '*$*$&% w -  ("("')`. . 0'*')X? 5 (H"# h"#("'*'*9$)'*(% ‰  z Œ DD{ Œ ± S { {B@® ‹ Š Š 4 Š ] Š ¯ C#z†B  { ³z&Ž>zj{  ‹ B Œ DG Ž zKD{ Ž#D  . L(Nœ! œ! ª  % € ž‚ o % o $*R 9„>%!_% ˜ |p("- 'UV2|?m.- 5 $*'* JK 2 ., $*(% ‰  G Š Ž {/° S { {B @® ¯ ‹ Š B!{/°@ Œ z Š { C Š F ]Š  ‹ B Œ DG Ž zKD{ Ž#D  . L(N¨œ ,¨œƒ, 0›!% € ƒ0‚ w % ~] % n,$g?j("'*L'* LT!"# (% ‰  X V  . L(;š 0œ¨!m0›!% € ‚ w % ~] 9 Rk% _ 5 '&% Ÿ`ƒœ!% . L(> š œ¨  ‘ T. -   w  ')   o  .0Ÿ4# ') ‰ (H#$&l79# 0› % € ›‚k76% 3 %/rq'*(" 0 ™ % „>% 2  # 976% w % m ("g% ‰ T./("("'*5')$*'UV2R?] '*(H"'*5 - | ("("- (f^h'U9p?&-$UV2 .,("(% 9S i ¨ ª ¡ ª ¤M ¨ƒš !¨ ª n›œ,% €U0‚>3% 1 #2,/76% 35 ("("/ m% 79 :; ?mT. - #'*(% S { {/@® C Š F B!G"Dk@{ ° S_‹‹ ® zKD"° 4Š ³zˆŽ  žƒ,M)¨ ª  ª n0››š % €U0¨‚k76% :` !')#% Ÿ[ ` 'U h("'*=-$‡'*9?O7X')(",2 # '* (f'*9$*'* Z$*L'*% ‰  S ° @{ ŽDC;z†{ zj{/D@G 4Š ³zˆŽ  $*- T ªªª /. L (` ª ¨ šœ!  979  '*0$  - ™  (››œ,% ‘ k5') L;”') ("'UV2 w ,'* a2 n("(% €Uš‚ w %:pT h 93% Jar_%•(" '*g% r $l 'Uv 0'*X?   Jˆ. - ')'*|.,$*(hJ_kLT`. . #% ‰  Š G#T@® D Œ ± Š °C]F Š G ]Š  ‹ B Œ DG DŽ B!G#z Œ ¯ U Z  ‘  '*0L/” w „` 3- $U2 ª  % €Uœ0‚>3% ‘ % 7X'U# $*$g >% w '*/%,„N $U2 ("'*([?q5 -(" Jˆ?† ,"#N("'*L '* L % ‰  Ozj{/@{/Ž zˆ@® G#¯ ‹ ŒKŠ ³GH@ ‹ ±!¯  ª !% €U0ž‚`•>% 76% ™ 0  s I76% o % w  ,0 0% ”N("')Lb "2 .'* ?jN-  !'*0'*9'*9$)L`  a^[!(h?qT.- (% ]Š =kB {zˆŽ@ Œ z Š {C Š F Œ ± D S I ª ¡H ª ¤M ››¨ !›››!O›ƒ!%


Ÿ% =% ‘ % c8,T w % w % 9% „x(",')T! $/?j -  ,'*0')9.,$*(% ‰  G Š Ž ¯ ‹ Š CzjB! Š {_XhDCD"@GHŽ#±izj{ Œ g  0   ›  › ¨ % DŽ B!G#z ¯|@{/° Gz @Ž ¯

7

T




F


9 ( :

O

]

;