HAL Id: inria-00072836
https://hal.inria.fr/inria-00072836
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Hierarchic Normal Forms for Desynchronization
Jean-Pierre Talpin, Albert Benveniste, Benoit Caillaud, Paul Le Guernic
To cite this version:
Jean-Pierre Talpin, Albert Benveniste, Benoit Caillaud, Paul Le Guernic. Hierarchic Normal Forms for Desynchronization. [Research Report] RR-3822, INRIA. 1999. �inria-00072836�
ISRN INRIA/RR--3822--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
!"$#&%' ()%+*,.-")%
Jean-Pierre Talpin , Albert Benveniste , Benoît Caillaud , Paul Le Guernic
N˚3822
December 1999
THÈME 1
-/.10/2435768.:9;9<.>=%0/?8@(682BA>C D?FE."9;GIHJ."2 KL.:2(68M;G<.NCHO.:2QP/RFGTSU0/6F?8?V0XWQYZC 5%0/WQ?\[].^_WQ."9<2Q6F`1a
bc+deUfUgihkj]l;mnf;oqpsrTft,mnusmvt$deUf;m
wx$y{zvft$m|}~Vt$x;w oqeJ}Xo
j,o{}}/yqxnt\sf7xnf<cfxcf "q:qh%f;fe/fx7g<q"7hk1}Xo{qf<m
T(;qq o"mf<7yq Oo{ f<o{x$ fx*¡yqx$¢L¡f}xnf<mf; :t4o{ s~£sf}tncOm$p+m$mn y" 7y{¤t$cf¥x$f¦ot$ y" +mc+ }+m
/ftv¡ff; §mnu1 +cx$yq 1u>o{ +§oqmnu1 +cx$yq 1uq¨U©1eJ}+ fªeUyssf¦m«y{¤Xyqtnc}+oqx$o"s "eªm%oqxnfJ}x$f;mnf :tnf< ¬o{ X
¡f_mt$ot$ftncf;yqx$feªmª¡]c¦cqpXo{xo{ :tnf;f®¯°°$±$®²ª³q±´µ¶L®$·s°n¯¶X¸ ¹<º²8¸»¯¶+%eUf;o{ + t$c+otTtncf_y"xnq +oq
mnu1 +cx$yq y"p+mmnfeªo{ :t$;m;o{ ª/f%x$f;yq +mtnx$p+t$f;J¤¼x$yqe½tnc+f%x$f;mnp ty{¤ t$c¦mf;mnu: Xcxny" ¾;ot$ y" *¨4bc+m
t$cfy"xnuo{ /fIp+mnf;oqmo+oqmnm7¤¼yqxyqx$xnf<ts¦mvt$xnpst$f;yssfI"f f;x$o{tnyq *¨Ibc+fI}x$f;mnf :t7}+o{}/fx
}+xnf<mf; "tm¥o f¡¿+ot$oOmvt$xnpXtnp+xnf"qt$cf7·s¸»±°$º°n®·1¸»®¶/¯{°ÀUº{Á¯{°À¤¼yqxo7tnxo{ Xm tnyq Ix$f¦ot$ y" *:¡]ccTm
+mtnx$peUf :t$oqX TeU}feUf :tn Otnc¦mtncf;yqx$uq¨(Ãfi p+mtnxotnf,tnc¦myq ToU©:totnf<c+o{xnt$m¥fro{eU}fq¨ bcf
¡]c+yqf«oq}}x$y"o"cT¦m eU}feUf :t$f; t$cfUÄ/żÆ4Ç È¬ÉUy"eU} fx<¨
Ê>Ë:ÌLÍ$ÎÏ Ð(q mnu1 +cx$yq y"p+moq qpXo{qf<m1sf<mu1 +cx$yq + ¾<otnyq ¬1mtnx$ +pstnf<yssf«qf +fxotnyq ¬¨
Ñ¦Ò ÓnÔVÕ;ÖÓ]×(ØÔVÙ8ÚÛ
Ü*ÝßÞFàâá8ãä$ÝßåÞFàæã<ç;è ãé]êë<ásìí*îLíãëïâàâívë:çðñòóôQõ*ívååíváöívìí£÷qçøÞ8ãåövíçùXé\ãàâï¦ú{ûÞ»áFüFåãé]íýïæãáFüFåãé]ínþ(àâÞ»àâáVã<ýÿ ÞçOí:ú
àâá! #"Þ%$Oàâá&"Þ
ãá'{ívívåUá8ëê<ê("Þ¼üFíìIàâåOêãÞ»ü'*)ü
í]ÿ"ïâï+", 4àâå-«êÞ%"/.Fívö£üFánú\õ¬ù0
ù21 ÿ ëåìívì34)65(ïâöã$ü8ívï¦ç
ùXá8ê<ÞFàü71
õ#89:7;=<?>ùXá8ê<ÞFàü4êÞ%"/.Fívö£ü(ù@Iôô4Aòð4B£ý
yqpXm%}+xnl<mf; "t$yq +m,p fJlt$p+sfUo{}}x$y{¤¼y" +sfsf<m%x$f¦ot$ y" +m\f; :tnx$f¤¼yqx$eªo{mneUf;mimu1 s~
c+xny" f;m%ft7oqmnu1 +cx$yq f<m/ft7 y"p+miltnpXs y" +miosl<mu1 +cx$yq +m$ot$ y" _sfU}xny"qxo{eUeUf;m%mu1 +cx$yq +f;m;¨
io{ Xm] y"mt$x$ooqpsrT}x$l;l;sf; "tm yqpXm]o:yq Xm]syq +lsf;m]xn tnd;xnf<mfLf;t$'¤»m,"oqx$oq "t$m$m$o{ :t¦oU}x$l;mnfxn~
o{tnyq Tsfi¦omnleªo{ :tn:pf,yqxmsf%¦ol;mnu: Xcxny" ¦mno{tnyq UftoOql; lxot$ y" Isf«yssf%mtnx$ +plf"¨f
xo{}+}Xy"xt]mf7yq +f :tnx$fimnpx]f;m]mtnx$p+t$px$f;m]sf7sy" lf<m]oqsl:p+ot$f;m}Xy"px\f«}x$yq+ d;eJf"Umno"yqxf;m
c+ l;x$oqx$cf;m7cy"xnyq"f;m;¨fTtnxoo{¥o{}}/yqxntnf sf;mlleUf :t$mtncl;yqx$:pf<m7 y"pqf<o{psrmpxO f<m7t$f;cs~
+:pf<mpstn ¦mnlf;m,o{ +mf7y"eJ}+ ¦ot$fpx«Ä/żÆ4Ç È¬É+¨
Ï < Í "! ¦o{ +"o{"f;mmu1 +c+xny" f;m;ssl;mnu1 +cx$yq ¦mno{tnyq *1"l l;x$o{tnyq f«yssfs¦mvt$xnpl;fq¨
; Ï Ð ({Ï
»<"(;
*; Ë 4s< Ë ! !Ë "
¨ g$#(x$mt,otntnf;eJ}t$m ¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ %
¨ w¥xnf<mf;x 1 Jmnfeªoq "t$;m'& s¦mnp+m$myq o{ + }x$yq}/y"mnf;my" ptnyq ¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨
¨ bc+f7¢qfuTsf<o ¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨
Ì
4 Ï Ï ()(
¼Ï Ì ; Ë +*-,/.',10 2
3 1 Ë1Ï Ì Ï54 Ð Ë Ì
¬ Ï
F;1Ï 5
6 ¨ g %f;mnu1 +cx$yq ¾ ,.', +o{ X b4¡y7#+p +oqeJf; :t$o{¬wxny"feªm¿¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ g
6 ¨ |¥ +syscx$yq 1uTo{ X j]f~Vmnu1 +cx$yq ¾;o{tnyq ¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ g<
6 ¨98vmnyscx$yq 1uqso{ X©1u1 +c+xny" yqp+m;:%mu1 +c+xny" yqp+myqeU}/y"mn't$ y" +m ¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ g 6
"<
Ë
s»
Ï !
4VÏ
«1
Ë
q+
ËÏ54
ϬÏ
!Ë ,/.',
>=
? ¨ g$@, f;x$oqx$c+ f<mk¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ g
? ¨ Aiftt$ Ut$cfO·1¸»±°nº{°n®$·s¸»®J¶/¯{°ÀUº{Áq¯°ÀCBED«¤¼yqx\oOtnxo{ Xm tnyq xnf;o{tnyq GF ¨7¨«¨7¨7¨i¨7¨ g<
=9H
Ï ! Ï 1»1Ï
! !
Ï »1
5
%+¨ g$@, ª >oJc f;x$oqx$c1u¨7¨«¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ q
%+¨ y"eU}Xy:m tnyq y{¤Qcfxo{xc f<m«¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ q
%+¨ %¦mnp+mnmnyq ¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ 6
%+¨6 y" +o{tnf; +ot$ y" yq¤4cfxo{xcf;m%¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ ?
I < Ë sË ª Ð Ë Ð ÏKJ » Ï ¬ Ï Ì L=
s¨ gAipXo{xm¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ M%
s¨ cXo{xoqt$fx$ ¾; +Of; +syscx$yq 1uª¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ :
s¨ cXo{xoqt$fx$ ¾; +O¦myscx$yq 1u§¨7¨«¨7¨7¨i¨7¨«¨7¨«¨7¨7¨«¨7¨«¨7¨i¨7¨«¨7¨7¨«¨7¨«¨7¨«¨7¨7¨i¨7¨ q
N < Ë
s»
Ï !
4VÏ
O
1
Ë Ë Ë
!"
Ë
7
(;q1
Ï Ë
QP Ë 5R
2TSJU Ï 1 Ë *;s Ë (s; Ë V!! Ë
'
WR
s Ì
ÐX! Ë /! Ë q1ZY Ë
[!\! Ë
Ð\ !4 Ï*Ï4]Ï4 1 Ë1Ï Ë "
L3
] ^
_a`b7cedGfg\hi
©su: Xcxny" yqpXm }x$yqqxo{eUeU kj
6
<+"g<l:cXoqm4Xf;f }x$yq}/y"mnf;7o"m¬oq fmIf :tQo{}}x$y"o"ci¤¼yqx*t$cff;mn "
yq¤¬x$f;oqtnqfio{ +Txnf<o{ ~Ft$ eUf«musmtnfeªm;¨b8VtcXoqmXf;f ¡]fuª}p ¾;f; spXm Otncf«¦sf;oq ¾f<I}¦t$pxnf
cXoqfI/ff; oqxnf<mnmnf;§t$y_tnc+mUo{}+}xny:oqc*¨ 8VtUc+o"m/ff o{x$qpf<§tnc+o{t; "fx$u¤¼x$f:pf; "t$ u" xnf<o{ ~8 ¤¼f
oqx$c+'t$f;t$px$f;msyU y{t\y"Xf;uªtnc+f7sf<o{ eUyssf¬y{¤4}/fxn¤¼f;t,mu1 +c+xny" :u"¨
@,y¡fqfx<+mn eUoqxn tnf;m%o{ +¤¼y"xneªoq¬ ¢sm%Xftv¡f;f _mnu1 +cx$yq 1u oq +>oqmnu1 +cx$yq 1uIc+o"fo{xnf<oqsu
/ff; s¦mnp+m$mf<« 7t$cf¥ tnfxot$px$fq;tnc1p+m"p+f;mtnyq tnc+f¥y qf;x$mneJ}+ +f; 1¦myq 7yq¤ nv¾;fx$ytneJfpy"eO~
}+pst$o{tnyq oq + +mt$oq :t$o{ +fyqpXm¥x$y"o"o"mvty"eJeOp ¦o{tnyq *¨(|¥o{x$uª}+o{}/fxj
?
l* s¤¼yqx$eªo{ uªs¦mnp+m$mf<
t$cfJ ¢_/ftv¡ff; }/fxn¤¼f;tmnu1 +cx$yq 1uoq +>t$yq¢"f s~V+oqmnf;oqmnu: Xcxny" yqpXm,o{t$o~+y¡ ftv¡y"xn¢sm;/mnff
}+o{xntn¦p¦o{xmnf;t$ y" t$cfx$f *¨ bcf+xmvt¤¼yqx$eªo{ o{ X sf;f}mvt$p+suT;o{ Xfi¤¼yqp+ +T j glV¨8Vt\f<mv~
to{¦mcf<m]oU}x$f;¦mnfix$f¦ot$ y" /ftv¡ff; >myq~V;o{ f<I¡f'~£ys¢qf; mu1 +c+xny" yqp+m¤¼p Xtnyq Xo{*}x$yq"x$oqeªm
oq +Ttncfmnp+mnft\yq¤7o{c+ ftv¡y"xn¢smo{eUf; +o{fitnyinp Lfxn~8f;m$m pif o{p+ot$ y" *¨
©1 +f«tncf; *stnc+f7m$mp+f7y{¤(mnu1 +cx$yq y"p+m}x$yqqxo{eqnnsf;mnu1 +cx$yq ¦m$otnyq Wp,c+oqm/ff; qf<mvt$ :otnf<
1uTmnf "fxo{ o{ptncy"x$mojgqg{Xg{+s/ 6 Xqs grl8+mnff jæl*¤¼y"x\oJeJy"xnf7sft$oq f;s¦mnp+mnmnyq *¨
8£ jæ:M% l+¡f]cXoqf}xny 1¦sf;Jo{ Ufr:t$f +mnqfqq Isf;}stnc¬"o{ Xo{u1mn¦mQy{¤/tncf] +¢1mXftv¡f;f ªmu1 +c+xny" :u
oq + oqmnu1 +cx$yq 1uq¨_bc+fT}x$yq}/y"mnf; 1¦myq yq¤,oqmnu: Xcxny" 1u_f +yqeU}+o"mnmnf;mmtnx$ +pstnf< musmtnf;eUm;
¡]c+c y " y"+o{«mu1 +c+xny" ¾<ot$ y" Bmvtotnfmoo{¦o{fq,oq +¿yqeUep+ ;ot$ y" +m :{oqtnyq +mIoqxnf y{t
+mt$oq "to{ f;yqp+m;¨bcm,fr1tnf; +mn y" _o{ y¡\mp+m\tnyIcXo{ +sf +y"eU} ftnff;mn " +m/m}/f;/ot$ y" +m;+}x$yq}s~
f;xt$ f<m"o{xc't$f;tnpx$f;m;qo{ Xfr1f<psto{f]}x$yq"x$oqeUm; ªo«p ++f<O¤¼x$oqeJf;¡y"xn¢L¤¼y"xXyqtncªmnu: Xcxny" yqpXm
oq +To"mu1 +c+xny" yqp+mmf;eªo{ :tn¦m;¨ bcf7o{/y qf,}Xo{}/fxm qf<mvt$ :otnf<ª }+oqxt$p¦o{xtncfi¤¼yqy¡] Otv¡y
¦m$mpf<m]x$f¦otnf< tnyIsf<mu1 +cx$yq +m$ot$ y" *s +o{eUf; uo& "!$#4·+±¶§¸¦´O³q±´µ¶/®·1°n¯{¶+¸¦´º²8¸»¯¶ °n±%±°²8¸'&Á±L¯°Oº
´¸ß¶)({Á ±«´µ¶L®$·s°n¯¶L¯1´*/°n¯+({°$ºÀ-,./oq + 0/1!2#4·+±¶>¸¦´ºJ¶/±²#¥¯°43ª¯Â\´µ¶/®·1°$¯¶/¯51´6L°n¯4(q°nº{À´«°n¯7&%1´² ²V¯
²¼·± ³q±´µ¶/®·1°n¯{¶+¸¦´º²8¸»¯¶B¯vÂI®¯{ÀOÀ8s¶+¸»®º²8¸»¯¶+´9, bc+fª f¡½ y{t$ y" +m«y{¤±¶/³q¯<®·1°n¯{¶+µªo{ + ¸¦´¯<®$·s°n¯¶Xµ
¡fx$fU :t$xnyssp+f;tny_oq +mn¡f;x"p+f;mtnyq +mUgIoq + xnf<m}/f;tnqfuq¨T| +syW:8vmny1c+xny" :u_oqxnfU}x$yq}/fxntnf;m
¡]c+cUoq O/f]cf;¢"f;y" t$cf\mnu: Xcxny" yqpXm4mn}Xf<Xo{tnyq +m;{}x$yqx(tny7sf<mu1 +cx$yq +m$ot$ y" o{ +Jyssf
mtnx$ +pstnyq *¨(| s¤¼y"x$ +%| Xsy>:r8vmyscx$yq 1u, Uo,""f sf<mq OmQoq Of/mª f; :t(¡ouitny«o{pst$yqeªot$;o{ u
mnu1 :tncf<m¾f,tncf«mnc+f;sp "mo{ +I}xnyqtnysy"m f;f;sf<ª¤¼yqxy"xnx$f;toqmnu1 +cx$yq y"p+my1fis¦mtnx$ ptnyq *¨
8£ ªt$c¦m¥}+oq}Xf;x¥¡f\ "t$xnysspXf,mnp t$o{+ f,+ot$omvt$xnp+tnpx$f;m¤¼yqxcf;¢1 7| +syW:8vmnyscxny" 1uqqoq +U¡f
}+xny 1¦sfyqx$xnf<m}/yq + %o{qyqx$ tnceªm;¨4bc¦mQoto%mtnx$p+t$px$fq{oq f;U·1¸»±°nº°$®$·s¸»®i¶/¯°ÀªºÁ¯{°À;:.<=?>A@
¦mioI f;¡ ¢1 +y{¤¥sf<¦myq soqqxo{e¨ 8Vt«¦m%oT yqx$eªo{4¤¼yqx$e ¤¼y"x,t$x$oq +mn't$ y" _xnf;o{tnyq +m;/'t7sy1f;m% y{t
x$f:px$f,o{ 1uU}x$ y"x o{x$¦o{f,y"x$sf;xn X¨a8Vt]sff;} uªfrs} y"'tmt$cfiep tn¦ys¢ª +ot$pxnf%y{¤(©su: Xcxny" yqpXm
b4xo{ +mn't$ y" B©1usmvt$feªmB:,.', @,o mneJ}+ f_eUyssf;\¤¼yqxmu1 +c+xny" yqp+mU}+xny"qxo{eªmªmp+qqf<mvt$f; 1u ,eU x
w¥ :p+f4o{ X>sm$pXmnmnf; jâs5% l8¨ 8£ ,/.', /mq +oqm,o{ >/f}x$f;mnf :t,y"x,o{Xmf; "t% _oª""f x$f;oqtnyq *¨
bc+f,}x$f;mnf :t;:{o{+mnf :tmt$o{tnp+my{¤¬oOmq Xo{+¦mo{+mtnxoqtnf<ªoqm t$m7®Á ¯<®+3DC¥-<=9>O}x$y :¦sf<m¥o;o{ y" ¦o{
¤¼y"xne ¤¼y"xmq Xo{¦m% §¡]ccy"xnx$f;mn}/yq +s y1¢sm«o{x$fJ f;mtnf< ¨FE,mn G<=?>+ | +y>:8vmnyscx$yq 1um
f/mIf :tnuTcf<¢qf; yqx];o{ Xfmnu1 "t$cf;mn¾f;*¨
bcf}+oq}Xf;x4¦mQyqx$"oq ¦mf<7oqm¬¤¼yq y¡\m;¨a8£ Umf<t$ y" O\¡f :tnx$yssp+foimeU}f©:tot$f;c+oqxtm¬frsoqeU} f
t$yªeUy{tnot$f7yqpx\oq}}x$y"oqc¬¨Qbc+f ,.', eUyssf;*m\xnf1XuIxnf<oq f; _mnf;tnyq +oq + tncfxnf<mp t$myq¤
jæ:%lo{x$fImnpeUeUoqxn¾f< mf<t$ y" 6 ¨B<=?>o{x$fU :tnx$yssp+f;§ mnf;tnyq
?
¬¤¼yqx7t$cfImeU}fx;oqmnf
yq¤,/y:y" f<o{ ,/.', ¨ %m ,/.', o{x$fTf:p}}/f; ¡]'t$cNmnu: Xcxny" yqpXm}+oqx$oq fy"eJ}/y"mn tnyq * ¡fT}x$y 1f
mf<tnyq %y"eJ}/y"mn tnyq +oq\o{qyqx$ tnceªm¤¼yqxIy"eU}pstn §tnc+fe¨X8£ mf<tnyq B¡f>s¦m$p+m$mUcy¡
<=?>_oq XfIpXmf< | +syW:8vmnyscxny" 1uq¨2<=?>¤¼yqx"f f;x$oq ,.', ¦ms¦mnp+m$mf< mnf;t$ y" §+¨ bcf
©1t$ot$f;c+oqxtmfro{eU}f¦m]x$f~£sm$pXmnmnf; _mnf;tnyq _++o{ +t$cf _yq + pXmyq +m]oq +}/fxm}/f;tnqf;m,o{x$f
x$o¡] *¨
?
h\f dea\h f k`\\
bc+fªeJyqtnotnyq Xm«¤¼yqxcy1y:m _©:t$o{tnf<c+o{xnt$mi¤¼y"xyqpx7fro{eU}fIo{x$fOt$cfU¤¼yqy¡] X¨[#( xmt;(©1t$ot$f~
cXo{xnt$mo{x$fioO¡]¦sfuI¢1 y¡] o{ +1mnp+o{/¤¼y"xneªo{¦me jg1% l8¨ \ X +mnf;y" + s¡f%¡]¦mncTt$yUyq 1 Xfitncf
x$f;o"sfxit$c+ot7yqp+x«tnf;c+ :pfJ¤¼y"xsmtnx$pstn >mnu: Xcxny" yqpXm,}x$yq"x$oqeªm,fr:t$f ++m«Xf;uqyq Xy"px7y¡]
ÄLÅ¼Æ¬Ç È4É%¤¼yqx$eUoq ¦mne jâ5lV"oq +Jf qf; O/fu"yq +Ot$cfgn£¤¼x$f Xc>pmnu1 +cx$yq y"p+m ,/. É jrlXoq + ,/.
jg 6 *g
?
lV¨
bcfª©:totnf<c+o{xnt$m,fro{eU}fOmncy¡] > 2+"px$fTg¡] mnp}}/yqxnt%y"pxim$p+m$mn y" tncx$yqp"cyqpt,tnc+m
}Xo{}/fx<¨Qbc+f7©1t$ot$f;c+oqxtm¥cXoqm¤¼yqpx\oq +1~£mvtot$f;m¡y"xn¢1 }Xo{xo{ f;M&Qo{ o{x$'t$fx<so{ Tf;eU'tntnfx<o{ X
a p out
1_bit_# 2_bit_#
h
a a
a a
sleep
sleep
out := 4
out := 2
out := 4
resume reset
p / sp_1
p / st_1
p / st_2
p / sp_2
running_1 running_2
out_1 / out := 2
out_2 / out := 4
a / out_2 st_2
sp_2
running_2
sleeping_2 running_1
a / out_1
sleeping_1
sp_1
st_1 out_2
st_2
sp_2 sp_1 out_1 st_1 sp_2 out_2 st_2
arbiter emitter
#4qp+xnfUgM& "!X²£º²£±$®·º{°²»´±$#:º{ÀLÁ ±1º¶L³TºI´®±¶/º{°¸»¯7C
tv¡yªy"p :tnfxm :&%('] t&)To{ ++*,']'t-)1yqp :tnf;x"@¨QÃcf >x$f;f: Jtnc+f7}p+mncs~8+pstt$yq eUf;m$mnoqqf/. stncf
oqxn+'t$fx«m¡] t$cf<m\t$yTt$cfU fr1t7mvtot$fq ox$poqx%¡ouq oq +_f;eJ t$m%t$cfªmvto{xnt8:1032 @,yqx«mvt$yq} :&04. @
eUf<mnm$o{"f;m«t$y¡oqx$§t$cfTtv¡yyqp :tnf;x$m;¨bc1p+mtnc+fTtv¡yyqp :tnf;x$mOo{x$fToqtnotnf< oq;y"x$s >t$yoq
:tnf;xnf;o1 >eUy1fq¨_Ãcf; oqtnotnf< Qf;o"c yqp+ "t$fxJyqp+ "tm7t$cfTyspx$xnf; +f<m7y{¤\fqf :t65X o{ X
x$ft$px$ +m%oq 87:9;2eUf;m$mnoqqf¡]c+f §xnf<oqc Ic¦m«¾f;xnymvtot$fq¨bcfUf;eJ tt$fx7f;eJ t$m%t$cfUxnf<mp titnytncf
f; :x$yq eUf :t<¨ yqtnft$cfUsLfx$f :tixnf<oqt$o{tnyq >eUyssf¤¼y"x,t$cftv¡yTy"p :tnf;x$m;X¡] tnc§o{ +_¡]'t$cyqpst
c+mtny"xnu :¼8¨f"¨ sx$f;mnpeUf,oq +ªx$f;mt$o{xnteUyssf@¨ ¿}/y"m$mn f%m$f; +o{x$y7msf;}tnf< ¨b8Vtmncy¡\m tv¡yOo"t$"f
}+c+oqmnf;m¤¼y"x]tnc+f<*;'] t&)sy"p :tnfx<o{ X y" f«¤¼yqx\tncf%('] t&)1yqp :t$fx<¨ yqp :t$ Itncf<5Im +qpx$f;1u
SO ¬ Ë74VÏ Ë Ð»;r»41Ï
8£ 8+"px$f]%¡f]mcy¡ o«smtnx$pstnyq Um$f Xo{x$ yi¡]'t$cJtncx$ff\yqeUeps~
a
a a
1_bit_#
st_2 sp_2
out_1 sp_1 st_1
1_bit_#
out_2
p
2_bit_#
out
2_bit_#
sleep
h
a
a a
a
running_1 running_2
p / st_2
p / sp_2 p / st_1
p / sp_1 out_1 / out := 2
out_2 / out := 4 arbiter
sp_2
st_2
running_2
a / out_2 a / out_1
sleep
sp_1
st_1
sleeping_1 sleeping_2
arbiter
out := 4
out := 2
running_1
st_2
sp_2 st_1
out_1
sp_1 st_2
out_2
sp_2
#( "pxnf &6\°s²£±¥Â¯{°n®±O³{¸¦´²8°¸'&%s²F¸»¯{¶ C "!$#&%')(+*,-).
+;otn 7mnf:pf :t$oq}x$y1f;m$mf<m ª¡]c¦cU¡fc+o"f" p+f;Otny"qft$cfxQt$cf\o{x$ tnf;x¥o{ +tnc+f\feU ttnf;x tny
¤¼y"xneo\mn qfq{mnu1 +cx$yq y"p+m<y"eJ}/yq +f :t;¨#ysp+m(y" «tncfqx$fui}+otcf;m4yq 65/0214243/%o{ +657$02142478 &
t$cfuTfrsc't\oUc+oq qf% tncf7 :tnf;xnf;o1 +1oqp+m J tnp+xn oOcXo{ "f% Tt$cf«c¦mvt$yqx$uªy{¤4}+xnysf<mnm
5/021423/ :¼ tnc+fmnf +oqxnyUy{¤+qp+xnfªg7¡f +xmvt\y"+mf;x"f 7 9;2:9<;=/1¡]cf t$cfm$f; +o{x$ yJy{¤ +"px$f
O¡f+x$mt]yq+mnfx qf 7:9;29<;5)@¨(Ãcf Xf«tnc+f7 y:mnmy{¤ mny{~£o{f;Tmnfx$¦o{ mf;eªo{ :tn¦m;¨
> Ë Ë Y'
\
; Ë !½ Ë
»q
8£ +"pxnf¡fTx$feUy "fªtncfp +f;mn xo{fTf /f<tªyqXmf;x"f;
Xqpx$fU1uT¤¼p+ u>smtnx$pstn ªt$cfOmnu1 +cx$yq y"p+m]mnfeªo{ :tn¦ma&t$cfOmtnf;}>m,xny:oq;oqmt,o{ +¦m\pXmf<
t$yo"t$ot$fOf<oqcyqeUep+ ;ot$ ©:t$o{tnf c+o{xnt;¨ u_sy" Ttnc¦m«¡fx$f;mtnyqx$ft$cfUmf;eUoq :tn¦m;/fqf;
" y"+o{uq¨b@\y¡f qf;x;"oqmxnfqf;oq f<U1uOt$cf%m$f; +o{x$ymc+y¡] ª +qpx$f,+:f<oqcImtnf;}T¦m¥ys¢1 X¨(bc+m
¦m\yq¤ßtnf; _p +o"f;}st$oqfoqm\oIeJyssfOy{¤ frsf<pst$ y" *¨\\ +_'t%tnpx$ +m%yqpst\t$c+ot%tnc¦m\¦m%p f<f;m$m$o{x$u oqm
¡f7mc+y¡¿ fr:t<¨
a
a st_1 sp_1 out_1 st_2 sp_2 out_2
2_bit_#
a
1_bit_#
p out
h
out := 2 out := 4
out := 4
st_2
out_2
sp_2 st_1
sp_1 out_1
out_2 sp_2
st_2 arbiter
sleep
sleep
a
a a
a
running_1 running_2
p / st_2
p / sp_2 p / st_1
p / sp_1 out_1 / out := 2
out_2 / out := 4
sp_2
sleeping_2
st_2
running_2
a / out_2 a / out_1
running_1
sp_1
st_1
sleeping_1
#( "px$fiL&°n±´±°<¸ß¶A(I´²£± ´±Àªº¶X²F¸»®´%C, *' %)(! %, <(<!:')(:%, ,-!)(%!
4 42 !#"& $% &' ($ )$ * $%+" 4,$%
gq¨]j]f¤¼f;xnx$ It$y +"px$fJs/¤¼yspXm,y" _tnc+fJsy¡] 1¡o{x>y"eJeOp ¦o{tnyq +m/5&-8032475- 04. 75 &tnc+fu
o{x$fo¡o{ tnf<«:u 57$02142478 º´µ¶/®·1°n¯{¶/¯51´Á'µ:cf; +f¡f¥ f;f;7t$y%frs} ¦ tnu«}x$f;mnfx qf t$cf" y"+o{
:t$fx$ f<o: O¤¼xny"e tnc+f7feU'tntnf;x,sy¡] tnyUtnc+fix$f;fqf;x;¨
bc¦m7moqcf "f;:utncfT¡ou_yq¤ :tnx$yssp+ >o/.¼Á ¯<®ºÁ´ +±°´²£±&0v(¡]ccc+o"m7oqmo> ys¢
tncfmp+}xnf;epe y{¤tnc+fTys¢1my{¤ 5- 03275- 04. 7514tnc¦mnvyso{mp}/fxmtnf}WpU¦mf;eJ tt$f;1u
tncf7oqxn tnf;x]o{ +T't] +s¦ot$f;mtnyJt$cf 5 7$0214278¡]c¦cmn " +o{/ t¦m]mnp}}/y"mnf;ªt$yJo¡o{ t tncf
y" +m¦sf;xnf<Tx$f;o"tnyq ¬¨
s¨]bcf ¬¬¤¼yspXm7yq tncf7 9;275y"eJeOp ¦o{tnyq )14oq"oq tncfIoqxn+'t$fx7¦mo¡oq't$ +T¤¼y"x'to"mu1 s~
cx$yq y"p+muq:o{ +I¡f,oq"oq U f;f;Ioonvyso{/mp+}Xf;x$mtnf;}>p&1:pst to{x$f;oqufrs¦mvtm1oqm¥¡fioq ªp+mf
¤¼yqxt$cm}+pxn}/y"mnf%tncf«eJeUf<so{tnf7mtnf} ¤¼yqy¡] Otnc+fif;eUm$myq y{¤4tncf 5ªmn " +o{8¨ bcf nmtnf;}>p
¡f7x$f¤¼f;xtnyªcf;xnf«¦mtncf7yso{*mtnf;}y{¤¬t$cfo{x$ tnf;x;¨
bc1p+m(¡fyq u« ff<7t$yiyq qf;xt4tncf 7:9 275,f qf; :t( :tny%o%/y:y" f<o{ mnq +oq"¡] tncUys¢i¦sf; "t$;o{
tnyªt$c+ot%y{¤Qtncf eUeUf;s¦ot$fmtnf}¤¼y" y¡] UtncffeUm$mn y" yq¤5+/o{ +f; +yssf<m 7:9;2475 1¦oUtncf
2 /(93Jyspx$xnf; +f<myq¤4t$c¦m]Xy1y" f<o{ mq +oqF1¡]c¦c¡f«¢"ff}oq 7 9;275X¨
y"eU}+o{x$ + ¡] tncG+"px$fU+4¡fªmf;fUtnc+o{t;(¡]'t$c yqpx7 +f¡my" pst$ y" **t$cf5/021 243/m ys¢"f;§yq s~
u ¡]cf; N¡o{ tn _¤¼y"xJtncff;c+y :¼/y1yqf;oq @mnq +oq 7:9;275+¨Ã§fc+oqf }xny"}Xy:mf<¿º¶¿º"7LÁ渻®º²8¸»¯¶32
³"±+±¶/³q±¶+² /°$¯²£¯;®¯Á0("±¶/±°nº{²F¸»¯{¶ /tnc¦m]¦m] p+mvt$x$o{tnf<T tncf +"px$f 6 ¨
convention out_2 : out_2=tt a_st_sp : "local superstep"
sp_2 out_2
st_2 a
a
a_st_sp
out
sp_2 st_2
2_bit_#
1_bit_# out_2 := tt,ff
p
a
h
arbiter
st_1
out_1
out := 2
a
a a
arbiter
sleep
sleep
a / out_2
p / sp_1 p / st_2
running_2
p / sp_2 p / st_1
running_1
out_2 / out := 4 out_1 / out := 2
sp_2
1_bit_# 2_bit_#
out := 4
arunning_2 sleeping_2
st_2
sleeping_2
sp_2 running_2
a / out_2 st_2
sp_1
: blocking
#(qpx$f 6 &J±´µ¶/®·1°$¯¶+¸ ¹¸ß¶)( 5702142780C ! ' ! , % $! <(<! 57;0327,04. % $! !$'6*' ( ,-!
*( % % % ,, ( )!'*4'6 ( )! *' <(%')(<$ 5- 032%- 04.%' *(&*' *, %)(<! '$*, $ ( ! "! ( ! !
!)!' (< % ! ! !' ( *' ( ! , 4' *! ! !)%, (+*4'. ! !- ! *(6 ',! 4'*"-! 6( )!# !),-! (+*' ( )!
( *!5&-8032 - 0 . .$ "7:9;275 % $! !$' , 4')! (<! % # ! ! *4'%(< $ 3! %'. > *# *, *(&
!'* ')(#* ( ( !*)(%)(<! , % (< ( ! + ,-(+*4' $ 57;0327,04. *' ( !5/0 14243/ % ' $( $! !$'
# %! !,!*,)*( .
&- .0/ 21 3
bc+m(¡oqm+zvp+mvtoq fro{eU}fq+pst 't +s¦ot$f;m(¡]c+o{t(¢1 +yq¤tny1yq1¡f +ff;tnyieªo{¢qf¥tnc¦mQmusmtnf;eUo{tn¦{¨
Ãc+f oT}x$y1f;m$m,¦mi¡oq't$ +I¤¼yqx«mtnep(¤¼xny"e t$cfJf 1 x$yq eUf; "ti §o{ o"mu1 +c+xny" yqp+m,eUy1fqL¡f
+ff; t$yJf; +mnpxnfit$c+ot,oªmnyqxntyq¤Qokn:Á ¯<®ºÁmnp}/fxmvt$f}>p«mt$x$oq +mneJ tt$f; +xmvt<s¤¼xny"e ¡]c¦ctncf7}x$yq}/fx
mnu1 +cx$yq ¾;o{tnyq §y{¤]t$cfTy"xnq +o{mvt$ eOp oq Xf ¤¼fx$xnf< 1ut$cfTx$f;fqfx¡]'t$cyqpstJxnf<my"px
t$y§oq 1u§" y"+o{ys¢1 eUf;c+oq mne¨ ,mJ +s¦o{tnf; +"pxnf 6 ¡fc+oq tnyºq³q³mnp+c oyso{
mnp}/fxmvt$f} yqxsfx«t$y_mu1 +cx$yq + ¾;fOt$cfIx$f;f}st$ y" §yq¤eUf<mnm$o{"f;m 5- 032%- 04.-71u_t$cf 57$021 278/¨
4 tncfy{t$cfxUc+oq + ¥mnp+c oyso{mnp}Xf;x$mtnf;} t$y§mnu1 +cx$yq ¾fTtncfxnf<f;}stnyq Ny{¤/7:9;2751utncf
5/021423/O¡o"moq x$f;o"suUooq ¦o{+ f"1o"m5/021423/J¢1 y¡\mt$c+ot 7:9;2475Joq T/f%x$f;fqf<Iyq + uU¡]cf; cf
cXoq feU'tntnf<>o{ +5+¨t#+xny"e tnc¦m :p¦¢To{ Xo{u1mn¦m¥t$cf«¤¼yqy¡] ªyq + p+mnyq +mfeUf;xn"f &
j]f;o"my" y" Itnc+fi +f;mtn Oyq¤4ys¢sm:» eU}¦ot$ y" Tyq¤4}x$f;mnf +f:{o{+mnf +f\/ftv¡ff s/f;xnf; "t
mq Xo{¦m+@i¦m«tnc+fI+oqmn¦Jtny1yq8¨ b4ytnc¦mf; +¡fImc+oq ¥ :tnx$yssp+fIo>myq~V;o{ f<·s¸»±°nº{°n®·1¸»®¶/¯{° 2
ÀUº{Á+¯°À ¤¼yqxmnu1 +cx$yq y"p+m«m}/f;X;ot$ y" +m¬¡]cceªo{¢"f;mit$cfª f;mtnf<mvt$xnp+tnpx$fUy{¤]ys¢1m
¤¼p u fr1}+ ¦ t;¨ bc¦mJ f;mtn yq¤,ys¢1mJoq /fT¤¼y"xneªo{ueªo{ + }p+o{tnf; tny§o{pst$yqeªot$;o{ u
mu1 :tnc+f;mn ¾;f%t$cf n ysoq*mp+}Xf;x$mtnf;}+m p¨
b¬y}xny "ftncf,yqx$xnf<t$ f;m$m(y{¤ yqpxo{}}x$y"o"c*{¡f+xmvt f;f;ªo7mnfeªo{ :t$¤¼xo{eUf¡yqx$¢ ª¡]c¦c
mu1 +c+xny" :u_oq +§oqmnu: Xcxny" 1u_o{ §/f«zvyq "t$ uc+o{ + f<§oq +tncfª}x$f;mnfx ot$ y" y{¤]mnfeªo{ :tn¦m
oq /f7}x$y qf;*¨
bc+mtoqmn¢Im]tncfmnpszvf<t]y{¤(tncf7x$f;mt]y{¤4tnc¦m]}+oq}Xf;x;¨
7ef [`bieidG ` G\h \hi '\
Ì
4 Ï Ï 4G(¥
1»1Ï Ì ; Ë *-,/.',10
Ãfo"mnmnpeUfo qys;o{p¦o{x$u¿¡]cc¦m,oªmnft,yq¤
tvu1}/f; o{x$oq f<m¨N\tvu:}/f;mUoqxnf eU}¦ tnu fr1tnf; +sf< ¡] tnc om}/f;oqf; f;eUf :tO¥ "t$fx$}x$ftnf<
o"mªº7&´±¶/®±¨O,eJy" tncfJtvu1}Xf<mi¡fUy" +m¦sf;x;Lt$cfx$fJoqxnfOtnc+fOtvu1}/fOyq¤60s°n±J´¸({¶LºÁâ´%¡]'t$c§sy"eªo{
. ]o{ + t$cf &¯;¯{Á ±º¶ tvu1}/f_¡] tncBsy"eUoq
. :¼x$f;oq ,Xyqtnc tvu1}Xf<mIo{x$f>fr1t$f +sf< ¡]'t$c tncf
mtn qp+mncf;ffeUf :t @¨OÃfªsf%+ fªo´²£º²£±Jtny/fUoTtvu1}Xf~Vyq +mn¦mvt$f :ti :tnf;xn}x$ftot$ y" y{¤,
o"mnmnq >o o{pfªtnyf;oqc o{x$¦o{fq¨ ÃfTf yqtnfI1u! t$cfTmnftyq¤oq mvtot$f;m;¨e#+yqxo>mnp+mnftyq¤
oqxn¦o{f;m#"%$&,:o'"«~£mvtotnf]¦mo%tvu1}Xf~Vyq +mn¦mvt$f :t :t$fx$}xnft$o{tnyq yq¤("I¨ bc:pXm o)"«~£mvtotnf*,oqm$mq +m
o oq p+f,+-/.(tnyTf<oqc o{x$oqf)- mnft'"1/tncftnp}+ fOy{¤o{pf;m%oqm$mq +f;tnyTtncfJmft%yq¤ oqxn¦o{f;m
" ¦m\sf; y{t$f; :u,+"0.V¨
çfsf1X f7o !/µ¶/®·1°n¯{¶/¯51´ °nº¶+´¸ß²F¸»¯{¶+!Xµ´²£±À :,.', @tnyUXf7oOtnp+} f B21435" 76 F8yq Xm¦mvt$ +
yq¤tnc+f¥¤¼y" y¡] +%y"eU}Xy" f :t$m1&"¿m(o + tnfmft(yq¤tvu1}Xf<º°¸»º7&Á ±´ 6 ¦mQo{ Oo"mnmnfxntnyq 7y" "7~Vmt$o{tnf;m
cXo{xoqt$fx$ ¾; +\tnc+f,mfty{¤Q¸ß¶+¸ß²8¸»ºÁX´²Vº{²V±´
,9:91 6: o{ + F¦mQtnc+f²F°$º¶´¸ß²8¸»¯¶ °n±Áº²8¸»¯¶x$f¦ot$ «}+o"mvt
oq +px$xnf; "t'"«~£mvtot$f;m;(<;o{ +!" :u>x$f¤¼f;xnx$ ªtny/y{tnc§}+o"mvt>=oq +pxnx$f :t oq p+f;miy{¤ oqxn¦o{f;m
?"I¨ #y"x,frsoqeU} ftncfJoqm$mf;xt$ y" @?1A@ ;CB %mvtot$f;m,tnc+o{t,tnc+f o{pfyq¤@ ?O¦m,"xnf<otnf;x\1u %
t$c+o{ 'tm o{pf ?<;¥¨ 8V¤ED5<; GF91 FTt$cf ¡fm$ou tnc+o{timt$ot$f<; ¦m,o)F 2/°$±$³"±®$±´´¯°]y{¤mt$o{tnf"¨
b4xo{ +mn't$ y" +m]o{x$f«}+o{xm)DH<; IF*JK 2L ]¨E#+yqx*MN1ODH<; GFoJtnxo{ +mn't$ y" >o{ +P-PJK" o o{x$oq f"s¡f
¡]x$ tnfM>+-/.(14DH ; +-<. ,+-<.QF¨
°s¶&RTS)VU GW IX VYZYVY ¦m>o mf"p+f +fyq¤Jmt$ot$f;mmnp+c¿t$c+otKVU491 6 [ \^]`_
a D5Vb
; W IbcFd91 F/¨
H Ï ! Ï 1»1Ï bcfT®¯À ¯´¸ß²F¸»¯{¶Iy{¤(tv¡y ,/. , Be1 BdWef BXi¦m\sf1X f;oqm¤¼y" y¡\m'&
B W f B X 1 3H"
W#g
" X 76
Wih 6 X F
Wih
F X 8 :vg @
j
0¬á8ëãïâï)çlkãÞ»àæã/ïâívá ãåì Únmpo'Örqcs
kãÞ»àæã/ïâívá ãÞ»íëáFívì«ü "\Þ»ívÿ ívÞ(ü ",övëÞ»Þ»íåü¥ãåìt qcuØ
á»üVã$üFíváný 7
àâá(àâá¬íwvëàkãïâíåü
ü ""ëÞ4êÞFíváFíåüå "ü8ã$ü8à+"å"ý í
ãxkíê<ÞFí£ÿ íÞ»Þ»íìü",ö"åáFàâìívÞy>zãåìyç4.»ëá»ü {ívöãëá8í¥ü
í¥ÿ"Þ»éë<ïæãá7 í¥á
ãïâï 4Þ»àüFí
é "áFüFï)àâå>k4"ïkíQövëÞFÞ»ívåükãÞFàæã/ïâíváçÞFã$ü
ívÞ ü
ãå%êãáFü"åíváný0¬á8àâå -ü
íQáFü8ãåìãÞ»ìiå "ü8ã$üFà+"å #"ë<ïâì
ãxkíQÞ»íáFëïüFíì,àâå
ã'ëÞ»ìívå "ÿêÞ»àâé]ívìEkãÞFàæã/ïâívá4àâå,ü
íQÿ"ÞFéëïæãáný
bc+fyqeU}Xy:m tnyq m4tnc1p+m(t$cf}+o{xn¡]¦mnfy" zvp +tnyq Oy{¤X tn¦o{so{ X7tnxo{ Xm tnyq x$f¦ot$ y" +m;¨a8Vt mcy"p¦
/f7 yqtn¦f;TtncXot;+
,/. ,
yqeU}/y"mn't$ y" *s "t$fxoqtnyq Tys;pxmtncx$yqp+qcyqeUeUyq o{x$oqf;myq uq¨
>Ï ;1Ï 48Ï V,.',
#yqx«t$cfTyq qf; f; +fUyq¤]mn}/f;X;otnyq ¬ ,/. , ¡] c+o"fªo>mfty{¤«°n±ºq®²F¸±
oqxn¦o{f;m¡]xn tt$f &"eU}'t$ u oqpqeUf :t$f; ¡] tnc oqm$myso{tnf;Bº5:#"¸ßÁ渻º°µoqxn¦o{+ f<m/&Jtnc+f ¡]cy" f
yq +mtn tnptnf;mtncf%mft"y{¤ o{x$oqf;m;¨¬Ã§f,mcXo{+p+mnftncf,¤¼yq y¡] «qf; fx$¦ y{totnyq Xm Ut$cf,mnf:pf;Q&
n - )VYZYZY sf; y{t$f,x$f;oqtnqf oqxn¦o{f;m;"oq +
o{x$f\p+mnf;Ut$yx$f¤¼f;xtny o{x$oq f<myq¤*Xy1yqf;oq
tvu1}Xf"¨
¤¼yqxd-To o{x$¦o{fq)J
. sf; y{t$f;m t$m®Á ¯<®+3 &E+1 E. +-1 E.
¤¼yqxd-ToJx$f;o"tnqf o{x$¦o{fq sf +y{tnf<m'tm\oqm$mny1o{tnf<>´²Vº{²V± oqxn¦o{+ f"sf1+ +f;1u&
1 - !"#1$
;
o{pf;moq Xfqqf; Nt$y2 U + .7oqmª}Xo{xnt y{¤«t$cf tn¦o{«yq Xs't$ y" *¨ bcf; *% ¦m oq ¡ousm
}x$f;mnf :tio{¤ßtnfxit$cf Xx$mt%yspx$xnf; +fOy{¤-/¨i#4 +oq uq&('*) 1+ Ltncf;xnf¤¼yqx$f nnmvtotnf o{x$oqf;m\yq¤
mvtot$f oqxn¦o{+ f<m p, f;f; yqt\Xfyq +mnfx$f; ¨
%m\eUyssp¦o{x$'tvu m%sf;mnx$oq f"+fqfx$u ,/.', mncyqp+/f}/fx$eJ tt$f;t$yTsyI +y{tnc+ T¡]c f t$m%f 1 x$yq ~
eUf; "tm¥}Xy:mnmn + uJ¡y"xn¢1 +¨(bc¦m ¤¼f;o{tnpx$f\c+o"m /ff Tuqftsf; :tn+f;U ªtnc+f\ tnf;x$o{tnpx$f,oq +Um¥¢1 y¡]
o"mi´² s²8²V±°¸ß¶A(i o{x$oq +f«yqx]x$yq+p+mvt$ f;m$mjg;s4g;lV¨ #+yqx\o ,/. , B%Xmtnpstntnfx$ ª o{x$¦o{ +fi¦m\sf%+ f<
o"m¤¼yq y¡\m1&8V¤iR 1 ZU lW IX ZYVYZY ¦m\oJxnp+ yq¤ B%+mnyJm
R&,^1 VU .-0/ VYZYZYZ .-0/
1 243 5
U687:9<;&=
/">@?&A
lW .-B ZYVYZYV.-B IX .-*C ZYVYZYZ .-0C VYZYZY
¡]c+fx$fq{¤¼y"x %o{ Io{x$ tnxo{x$umt$ot$fq:mu1e/yq(.-sf yqtnf<mQtncf´¸ßÁ ±¶X²(´²£º²£±o"mnmnys¦ot$f;O¡]'t$c":sf%+ f<
1u
\ - JC" SED
- +-/. 1
.-G+V. 1 ,+I.
eUf<o{ >t$c+otUmvtotnfo{x$oq f<moqxnfª¢"f}stJp +c+oq qf<¡]cf fqf;xtnc+fxJo"mnmnys¦otnf<§xnf<oqt$"f o{x$'~
oqf;m_oqxnf oq+mf; :t;¨ 8Vt§mncyqp¦XfN y{t$f;t$c+otmtnpttnf;xn B o{x$oq +f o{y¡\m¤¼yqx_x$p +m}Xy:mv~
mnf;m$mn yq + uBo + tnf 1peOXf;x>y{¤O}+xnf<mf; "t>mt$ot$f;m;¨ çf mcXo{7xnf"p+ x$f tncf mnf:pf«t$c+ot_oq
,/.', ¡fyq +mn¦sfxªo{x$f>mvt$pstt$fx$ + o{x$oq :t;¨bcfuNmcy"p¦N +sf;f; m$otn¦m¤¼u& D5
; GFC91 FGF
D5<;
- H
F 91 F oq + Dc
- H
GFC91 F/¨Ãcf t$cm y" +s tnyq mI y{tTm$ot$m.+f;*¡f>fr1t$f + F
eU eUoq uTmnyt$c+ot,mtnpttnf;xn U oqxn¦o{ +f,¦m]mno{tn¦mXf; ¨ uTy" qf :t$ y" *1¡f7mnc+o{ meU} uT¡]xn tnf:
+mtnf<oq y{¤N - ¡]cf; eUf; "t$ y" ªoO}Xo{xntn¦p¦o{x\mt$o{tnf)7¦m y{t\x$f:px$f; ¨
I ! !Ë 4VÏ ,4( Ë P Ë
Ë ( Ë
çf¥ y¡§ :t$xnyssp+fmfqf;x$oq{meU} f¥fro{eU}f;m*tny] p+mtnxotnf
y"px\o{qy"xn tnc+eUm;¨Qbcf©:t$o{tnf<c+o{xnt$mfroqeJ}+ f«¦m]xnf<s¦mnp+mnmnf;T >mnf;tnyq ¨
! #"$&%')(+*(-,-%/.&0'1%%23'4$15%23'#0"6+71%809;:0<#0.=>?@A@ 'A
BDCFEGBDH4EGBDI
J KML6N
OPRQ
E *S1T8UWV EYX Z \[+]V EY^
,.= Q %:622Z$+'!_a`-.6%b%-#@$+7c2edZ=69+9;:0<#0.=f:622Z$+' Q _ g
@+702Z'=9h5! #"$#%!'i(+*(,%/.0'1%%23')$A%23'#0"6+71%3+9;:/<&0.=>?@A@ 'A
OjP B8HlkEnm
S1To3UpV EYX
Z \[+qV
EY^ KsrtN
`-.6%F@$+7c2a%'12udZ=69+9D_ g
v w
Gk` yx cG ef [`bieh k\hi
bc+f«mnu1 +cx$yq y"p+m}x$yqqxo{eUeU }+oqx$o"sqe ¦m]f;m$mf; :tn¦o{ uIc+oqx$o"t$fx$ ¾;f;To"m¤¼yq y¡\ma&
gq¨wx$yqqxo{eªm,}xny"qx$f;m$m 1o o{ _ + +'t$fJmnf:pf; +fOy{¤\°n±ºq®²8¸»¯¶´;&fz 1|{i}(L¡]cfx$f~{sf; y{t$f;m
tncf«¤»oqeU uTyq¤4}/y"m$mf7xnf<oqt$ y" +m;¨
s¨Ã't$c _oOx$f;o"t$ y" *sf;mnyq +moq /f«t$oq¢qf; y" t$cf7+o"m¦my{¤(tncfTºD&´±¶/®±y{¤ mnyqeUf«f qf; :t$m;¨
¨w o{xo{ f;qy"eJ}/y"mn tnyq 7¦m*qqf; 71u,to{¢1 +tncf}+o{xn¡]¦mnfyq {zvp +t$ y" 7y{¤oqm$mny1o{tnf<%x$f;o"t$ y" +m
¡]cf +f qf;xtncf;u oqxnf«y"eJ}/y"m$o{+ f &uz W f1z X 1 D?{ Wih { X F} ¨
8£ yq :tnxoqmt;Lt$cfU¤¼yq y¡] >oq /fImt$ot$f;o{/yqpt7tncfª¢1 +§y{¤o"mu1 +c+xny" :u>¡fªy" +m¦sf;x7 §tnc+m
¡yqx$¢o&
gq¨]j]f;o"t$ y" +m,;o{ yqt\XfOyq+mnfx qf<o{ 1uTeUyqx$fM&m +f yI" y"+o{¬ ys¢frs¦mvtmXqyq+oq¬mu1 +c+xnyq~
¾;ot$ y" +oqxnx$fxm]¡]c¦c +s¦ot$ft$cfOtnxo{ +mn't$ y" >¤¼x$yqe yq +fx$f;oqtnyq >t$yIt$cfU fr1t«yq fJo{x$f
yIeUyqx$f7yqXmf;x o{+ f"¨E8£ Xmvt$f;oq*XoUx$foq fOyqeUeOp ¦ot$ y" eJf<spe m%oqm$mpeUf< + >¡]c¦c
eUf;m$mnoqqf;m oqxnf] +y{t¥y"mt;:o{ + q¤¼yqxf;oqcJ +s:¦sp+oqXc+oq f;F"eJf<mnm$o{"f;m oqxnf\mnf :toq +Jxnf<fqf<
Otnc+fm$o{eUfyqxsfx<¨¬Ã§f;o{so]¯#Ttncft$y{t$oq u7yqxsf;xnf<mf:pf +f¥yq¤ o{pf;mQmnf :tQyqx(xnf<fqf<
yq >oJqqf; yqeUep +;otnyq c+o{ + f8¨
s¨]\+mnf Xfoq yqt/fsftnf;tnf< +o{ XIt$c:pXm\oq y{t]/f7p+mnf; tnyUfrsf;x$mnfiyq :tnx$yq8¨
¨ yqeU}/y"mn't$ y" NyspxmO1u eUf<o{ +mUyq¤%p ¤¼u1 + f;oqcN Xs1¦sp+oq +y¡ mnc+o{x$f;N/ftv¡ff Ntv¡y
}x$y1f;m$mf<m¨(bc¦mQeJyssf;mQ J}+o{xntn¦p¦o{x(t$cf\y"eJeOp ¦o{tnyq +m1oioqmnu1 +cx$yq y"p+m4p 1Xy"p +sf<
#8# 4 m;:mnp+cTo"mt$cy"mnf, 7o{c+ ª ftv¡yqx$¢sm¨Qj]f Xsf¾~"yqp+mtvu:}/f,yq¤¬y"eJeOp ¦o{tnyq Ioq To{¦mny
Xfoq+mtnxoqt$f; t$cm¡ouq¨
8£ t$cf«xnf<mvt\yq¤¬tnc+m\mnf;tnyq ¡f7mnpeUeªo{x$ ¾;f%t$cf«¤¼yqx$eªo{ x$f;mnp t$m¤¼x$yqe jæ:L% l8¨