HAL Id: inria-00074112
https://hal.inria.fr/inria-00074112
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,
On Modeling Consistent Checkpoints and the Domino Effect in Distributed Systems
Roberto Baldoni, Jean-Michel Hélary, Achour Mostefaoui, Michel Raynal
To cite this version:
Roberto Baldoni, Jean-Michel Hélary, Achour Mostefaoui, Michel Raynal. On Modeling Consistent Checkpoints and the Domino Effect in Distributed Systems. [Research Report] RR-2569, INRIA.
1995. �inria-00074112�
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
On Modeling Consistent Checkpoints and the Domino Effect in Distributed Systems
Roberto Baldoni, Jean Michel Helary Achour Mostefaoui , Michel Raynal
N˚ 2569
Juin 1995
PROGRAMME 1
13245670,89+:<;5*=&>/?A@
BCEDFHGJICLK&MONQPRCESUTWVXVZY\[]FOM^S\_`TQabUFHN"c$FdNQM^GeVXV
fabUC]ghG_`CjikIFZlmM^CEgUTVkVHY_`TnaobhFHN"B$MHeSM^NVXV
pUqsrWtZqmuv$vwx6y{z|qm}s~Ow}OqswX EuqunwXwX HEuo wX HwHrZOwXwk OqOwX wJuHwX| H wXvwX sqs^wX
pUqrwX |z5H
|uO]rWqsHw qw}s~OwXq}s~OwdWZWy¡ WO%xZWy{WEutZwX
¢£(¤k¥J¦§E¨¥Z©ª+uW}s«H¬uqmwXqqsrWqUqw}rWwXqs rW^w"ro®s~Ow+vrW sjO wJ }~^wXvwX Rr|wXO ^qw+®nuoOQ¯QrWwXquE}w
H sqO^w H swXv J°±QU}rW^ s ZOErZ~^w"rO}X}^qqwkE}wro®²u+®QuOqwWJ qwX srZqOtuH sqO^w
}rZvO^musrW'ruo&wXqqsrWqQ¯³®´qswXw tWrWEuoH muow6®´qrZvµ¬~O¶}s~}Xu$Ew|qwX sOvwJ'rOqsrOHE}w u}rWqsqw}
]wX~EuJHrWqJ°¸·+~Ow}s«H]rWHOt 'rWOw&ro®~OwwJ}~^O¶¹W^wX sr¸^Oq sOw~Ow$EuW}s«H¬uoqmºwXqsqrZq&qw}rZwXqH°
±Qs~O Eu]wXqJE¬+wOqswX wkdu'tZwXOwXquj®³qmuv$wX¬+rWq«&s~Eu|muo«WwX u wXvuH¶}E}]HOtv$ Ot&u]
rZqO~Euov$wX utWwk dsruW}k}rWOHJ°»rWsrWO ro®²v$ OtZ uE'rZqO~EuoO uqw|qwXH sw&H&}rWO s¶HwXqOt
uZOHrW]u+OEHwXqsdOtºvwJ}~]uO v¼uJWuo¶uoOwrZ½}s~Eu^OwX ¾uoE% swXvuoH¶} 'r®5v$wX utZwX °%¿~^
®´quv$wX¬"rZq«%ur¬ ÁÀEq sr smuswuEÂOqrZwus~OwXrWqswXv¼sr<HwkwXqsvOwî5uo4uq^sqmuoq% wkro®
}s~Ow}s«H]rWH &}rW^ swXHu]j sw}rW]jr%HwÀ]Ow®´rZqvuos~OwHrWv$^rwÄjw}°`ÅO^q~^wXq+¬+w
s~Or¬~Or¬^qwXHrWO s¸O^O s~OwÂOE}rHrWqHEusw4}s~OwJ}«H]rWHOt%utWrZq~^v }XuÆEwHwX }q]w
4rZOq}rZHwOu]% rZvw'wEuv$Ow&r®OE}rdrZqmHEuowÆ}s~Ow}s«HErZHs^t<uotZrWqss~Ov |~EuowkO Oqsw
HrZvOro¯´®´qswXwqsrWEuW}s«&qsw}rWwkquqswuo r'tWWwXR°
Ç$ÈHÉjÊËÌ]¦WÍU¤© ·+rWO s swXHLtWrZEu}s~Ow}s«H]rWH ºÎuov]rWqJÏ %~EuO]wXOwJZ¯n]w®´rZqwÐqswX¶urZrZqQ¯
O~]u%uEv$ Ot'vwk muotWwX JHrZvOr'wIJwJ}ROE}rHrZqmHEuowº}s~Ow}s«HErZHs^tutZrWqs~Ov JZ®nuOѯ
srWwXqmuoE}wWjH sqO^w$ H swXv$ °
Ò¶Ó&Ô
ÕnÖQ×Ø
Ô
Õ(ÙhÚÖQÛQÜÝ
Þßàá³âUãWäánåçæèäéêéèëjìçíããdàáQå³îïjðëåçñWî^òàéêéèàó]æêôWõjöjäXìçæè÷EøRîì³îäáQ÷³ñhùR÷åçæèàô"ú^ánàkõánäûìàòüåçñWî]ýOíáQàãdîsäô(þ]àûû"íôæèå¶ëZÿ
åçñWîUþÐãáQà´îs÷å]íôWïîQá÷sàôå¶áQäX÷åRà Qþ]ùöjý]øRý äôWï åçñWîýJú]øãánà³î÷så]íôWïîQá÷àôWïîQá÷àôüåçánäk÷å
Rà köjøjùþ]ù
ÞsÞ
¶ø Jù!Wþ]äûãíWìjïî+öjîäíéêæèîÑí"!#$øîÑôôWîìþ]îsïî&%'!)(JáQäôW÷sîøRàðdîÑánå³à+öjäéèïàôæWæèìRàô éèîä*kæêôWõòÃánàû+RæêãWäá-,
åçæêûîQôå´àïJæôòàá´ûäkå¶æè÷Qä+î.kæèì´å³îQûæèì³åçæè÷ä !/jôæ0*XîÑánìçæèå¶ëàò²øRàûî132däJäãæèîÑô54ä6!*kæèä7Jäéèäá³æèä.886!59,:8;=<"øRàûî!
¶å³äéèë=>]ñæèìäíWå¶ñWàáUæèì+äéèì³àìçíããdàáQå´îsï|ðüë'ä õánäôüåUàòåçñWî@?ACB
ÖEDGFHD AJIK&L
D
ACB5K
HêÕNMÕOH0HêÕ
Ó
D9PnÕ3Q-PERÕ
íôWïîQá÷àôüåçánäk÷å
Rà ; =;$ þ8
9 #)9U+
Ȥ ÈЩ ·+wquO]rWqs ÏHOwXqswX sw½uº¶u¸+wÀEOrZ w]rWH wqwX^q w¸^uO &wX & sd swXv$wX
qOwXEuqs °\}XuZHqwºtwkwXqmuoQ"HOwktWqmuoHwX vwX s muotWwX $vu]¹W]uH &wXwX $vwX s mutZwX rZqO~^wX^
wX s¾+w}q'wXO^w}rZEHrWºw}wX uqwwX s muoHwWREH¶¹ZEuH +O%wXO swXv&Ow&Hw]rWH Hw
qswXOq swr}kuH&wX }rW~wXqswXH^wX HrZOwW°OpUuoquowXOqs ZOOw+wÀ]OrW'®´rZqv$wXwHw QÏwIJwkHrZvOr
wX s^qrW]rW OwXw&wXwX wOwXv$OwX jÏêutZrWqs~Ov&wX qOwXEuoq w"wXwkqvEuorWºHw]rWH 'Hw&qwX^q w
}rZ~wXqswXH rZd^qOwX swXHOwX J°
`Ì]¥ü¤kÊm¨È © pRrWH 'Hw&qwX^q w}rZ~wXqwkds OqOw}]wHwXE}w¸}Xu^ muwHwÎRuv]rWqs]vwk muotWwX 'vuoH¯
¹ZEuods wk&vwX s mutZwX 'rWq^~OwXO RwÄjwXHrWv$OrEjutZrWqs~Ovw'OrW4}rdrZqmHrZOwWUsrWJwXquE}wuoH½+w¯
®nuo¶uoE}wX JH H wXvwX sqs^wX °
8 9 9$º;+
#,,+,:,+;,4"}rZvO^wXq sH wkv + +uu «'~]u+HZrWWwX qwX srWqsOt¾uo&wXqqsrWqѯ´®´qswXw uw|®´qsrWv
uo¸wXqsqrZOwXrW^ rWOwZ°=<UqqsrWqqsw}rZwXqº m}s~OwXv$wX uqsw&O Euo}¶uo ÃÀEwJHr?>@,A, uEB.C'DAE,+
wXqsqrZqqw}rZwXqGFêHÑ°JI=,A,+$,,+,:,+;,4" +Eu sw&rZuowkvOs^t5srvu«Zw+®´Oqs~OwXq+O w ro®~Ow
smusw ¬~O¶}~$~Eu jO s"]wXwX$®´rZOEr]w &wkqqrZq°^¿~O " ]rW s Ow ¬~OwXs~Ow EusOqw|r®s~Ow wXqqsrWq
uoE}rWO sw¹ZOwXE}wk "ro®O®nu^s h}Xuo]w}rZvOwXswX5uo wk wJj°H¿~OwXrZOw}Xu'qwXv$rWwU~^rW w+wXqsqrWqs "u]
wX]uOws~Ow H swXv rvrZwj®´rZq¬uqj° 6 Euo6®´rWqs¬uoqm|wXqqsrWqRqw}rZwXq quswXtWwX uqswEuo w rZ ~Ow
O swr®EwkqqrZq"}rZqqwJ}Otsw}s~OO¶¹ZOwX "uoE'}rOHwX orWqUwXqqsrWq"}rWv]wXO usrZOqsrd¶HOt sOOOwXv$wXHmuoq
H®´rZqvurZ°K&C'DAE,+3,,,L,+;D,4HWrZWwX JXÀ]q JW]uW}s«H^t5^rZOwrWqv$rWqswr®j~Ow^qrO}wX s wX
ro®s~Ow H swXvAr4uºOqswXHrZO & uswW¬~O¶}s~4 &~OrZEwJ4sr%EwwXqsqrZqQ¯³®´qwXwZ"]w®´rZqw¸uoswXvOsOtr
wOw}Owº®´^q~^wXqrZEwXqusrZO °+±QL~^ $ m}s~OwXv$w& &OrW$Ow}wX s muoq3sr%®´rZqwX swXw¸s~OwEuoOqsw¸u]
}rZO wJ¹W^wXE}wX ro®²uH~^w®nuoO JüuoE sr5qswXvrZw"uZ~OwwXqsqrZq °o¿~d^ vu«ZwX ]rW s Ow"sr qw}rZwXq
®´qsrWv uo4uqsOqmuoqº®nuoO v$OH%qwX srWqsOt¸s~Ow H swXvAr¸uo½u^OqrZOq¶uswOqswXHrWO & smuswW°
¿~Owk w ®´wJu^qwX |wXEu^w EuZ}s«d¬uq&qsw}rWwkqr'Ew}rZO ¶Hwkqwuo utZwXOwXquRqw}rZwXq$vw}s~EuoO v
sr¾uod'QHEw ro®j®nuOJ°CMr¬+wXWwkqHEuZ}«H¬uq'qw}rZwXq$OwXw N,+;,4:OOQ°wZ°ZwÄjw}sZw vwuoO
H¬~O¶}s~¸u& smuswro®"u&Oqsr}wX }ku]w muJZwºuE$¶uswXq qwX srWqswj°Å^rWqrZOmuoOOt& E}s~ºqw}rWwXqs
]rWH $rWOwro®~^wEu s¶}w}s~O^¹ZOwk P+'-Q°"±Q}rW^ s 3HwXswXqv$OOtE+HOqOt4u
}rZvO^musrWju$ wXr®rO}Xuo}~^w}s«d]rWH R´Q°wW°²u wXro®rO}Xuoh smuowX ' muJZwº uOw& srWqutWw5SX
®´qsrWv`¬~O¶}s~XO]rWu®nuOqwRrO}X}OqsqwXE}wWdu+qsrWw|EuW}s« }rWv$OOmuorW }XuEwqswX ^vwj°kzd sE}
Euoq +r® ]}~rO}Xuj}s~Ow}s«HErZds "v&^ ]wv&OsEu}rW^ swXH$rWqHwXq+~Euo"s~OwqswX Ov$OrZ&Ew
®´wJu OwW°]±QH®³rWqvudov&OEuo}rW^ swXE}%uv$rWOt'r}kuh}s~OwJ}«H]rWH wXO sOqwk s~Eu|~Ow'qwX sOvwJ
}rZvO^musrW¬UEw& swXvuods¶}Xu}rWqsqw}J°hÅ^rWqsvuo TuorW$r®~Ow&^rWrZ¸ro®6}rZO swXH'tWrWEuo
}s~Ow}s«H]rWH 5}kuEw®´rWO]&PFx7^U5H°
V uH¸utZrWqs~Ov +~EuJWw&]wXwX%^qrW]rW swºr}rZvO^w&}rWO s wkd'}~^w}s«d]rWH J°¿~^wX<}kuºEw
}¶uo ÃÀEwJ'Hsr5Q¬+rvu|®nuv$wX uZ}X}rZqmHOt r s~Ow}rHrWqHEusrZwkvOrWwJsr mu«Zw}s~OwJ}«H]rWH J°
±Q'~Ow5,DN'C",+5C' FWH^qrO}wX s wX }rHrZqmHEuow+wOO}sdkd v$wuO Rr®}rWHsqrWHv$wX utWwk
s~OwHwXswXqv$EusrZro®h~^wXqrO}Xuo}s~Ow}s«HErZHs rWqmwXqr&]wv&OsEu}rZO swXH°]ztZrWqs~Ov
s~Eu uWHrZO~O uoOOqrHuW}s~}Xu Ew swXwX¸uZ}]uu v$OqrZwXvwXHs rWquZOuOusrZO r®U EuoO ~^rW
uotZrWqss~Ov NFxXHrs~Ow¾}s~OwJ}«H]rWHOtOqsrWOwXvº°OÅOrZq5wJuW}s~¸^qrO}wX s ~Ow&¶uo 5}s~OwJ}«H]rWH mu«ZwXº
uo¬uJH U~OwrO}XuH smusw¬~O¶}s~'~OwOqsrO}wX +v&O s]wqwX srWqsw&sr è®u6®nuOqsw"}Xu^ wX + UqrZEuZ}s«²°
¿~^wEuo ¶} }~]uqmuZ}wkq s}|ro®h~^wY05,DZC",+5C'YFx5[O]xO]xWH "s~Eu+OqrO}wk wk 5u«Zw
}s~Ow}s«H]rWH v$rWqsw&rWq&wX &EwXEwkEHwXHH°M6r¬"wXZwXqUs~O uO^qrduZ}s~½}Xuo½]wHHw%HrºQ¬"r
}¶uo wk uZ}X}rWqHOtsr5s~Ow]rW sOwr}k}OqqswXE}w ro®²s~OwHrWv$OrwÄjw}NF]\H²HOqsOt qrWEuZ}«qw}rZwXqH°
¿~OwHrWv$Or&wÄjw}u^Ewuoq ¬~^wX½u$ ^O wX'r®^qrO}wX s wX J¬~O¶}s~¸~]uJWw&r Ew&qswX Ov$w%uJ®³wXqu
®nuo^qwWjqsrWEuW}s«ºOHErZOEHwJH¸¬~OwHwXswXqv$OOtu wX&ro®v&^Euo}rZO swXH¾}s~OwJ}«H]rWH J°
¿~Ow'À]q &}¶u s u s Ov$w]wX s v s¶}Xu~Euo~OwrWvOr&wIJw}}rWO¶ rO}X}Oq&uE ~^wX4u«HOt
wX^rWOtZ~ }s~OwJ}«H]rWH rZq"rWtZtWOt wXOrZOtW~$vwX s muotWwX + "OwJ}wX uqs$rWqmwXq"^rW+r'Ew ^Ww}swr
s~OwHrWv$^r5wIJw}F]7HExJ5H°^ wXOwXqudZ~^wvrZqw}s~Ow}s«H]rWH u]&vwk muotWwX uqsw rZqw$ smuoOw
srWqutZw~Ow wX s qrZ]uW}s«& "OwJ}wX uqsrHwkwXqsvOwu swXro®hv&OsEu}rZO swXH5}s~OwJ}«H]rWH J°
¿~Ow| w}rWE®nuov5u s Ov$wrWOsv s}ku~]us~OwOqsrWEuoOQr®~^w5}rZv&OOwwXWwXHE_®nuo^qw
ro®²uOqsrO}wX X_¾uoE_HHrWv$^r"wÄjw}X_ ZwXq}rZ w+r:TXwXqr]°±Qs~OwX wuotWrWqs~Ov$ Oqsr}wX swX "rZtrW^
®´wk¬3vwX s muotWwX FxW5H°±³®hu|®nuo^qwrO}X}Oqs ^~Ow|qrWEuZ}«qw}rZwXq$OqrO}wJHOqw ~Euo "srHwXswXqv$Ow®´qsrWv
s~Ow}s~Ow}s«HErZds OqswXHrWO s$muo«WwX]u' wX|r®v&OsEu}rZO swXH rO}Xuoj uwk ®³rWq+~Ow^qrO}wX s wX
¬~O¶}s~&~EuJZwr]wqswX uqswjHO^"s~O "HwXswXqv$]urZ OrZtW]uqmuoHwXw :",/,dOwrs~Owqs «
ro®rWvOr wÄjw}J°
Å^qrZv\u]wXqÑ®´rWqsvu]}wUErZHjro®HwX¬k~OwX sw"Q¬+ru^OqrHuW}s~OwX R ~Or¬%uwkd¶HwkdjsqmuZHwXrÄ&]wXQ¬"wkwX
s~Ow rWwXqs~OwuW$HOqs^tuH sqOOsw}rWv$OOurZuE~Ow|rWwXqs~OwuZHOqsOtuqw}rZwXqH°O·+rHrWqHï
Euowº}s~Ow}s«HErZdsOtuWOsrH qsOOwJ¸}rZvO^musrW}s~OwJ}«H]rWHOtZ jv$wX utWwrZtWtZ^tW u]
}rZHqrZOvwk muotWwX J~HO EwXqÑ®´rWqsvuoE}wX Ur®]®nuoOqsw¯³®´qwXw}rZvOOusrZO huoqw]wXEuo TXwJ'OqrZErZqrZ
srs~OwXq s TXwW°|º~Ow'rWs~OwXq ~Eu]jOO]rWº~^wrO}X}^qqwkE}wro®u'®QuOqwW^wuW}s~ºOqrO}wk «HOr¬ |~Ow
rO}XuR uw¬~O¶}s~v&O qsrWEuW}s«j°H¿u«HOt¾}s~OwJ}«H]rWH |uo^E}rHrWqHEusw¬uJv]rW swX
ZwXqº®´wk¬ rZwXq~^wuWÆHOqOtºu$®nuOqsw¯´®³qwXwH sqO^wÆ}rWv$OOmuorW R´wW°tE°U}s~Ow}s«HErZds vuJEw
u«Wwk¬~OwX$OqrO}wk wk uoqw|w5SX°]rWs~OwrO}X}OqqswXE}w'r®hu|®QuOqwWZ~^wqrZ]uW}s« ^rWN:,/,
tZEuquHwXwJr' E}k}wXw R´Q°wW°H rZvw^qrO}wX s wX }Xuo]w qrZw$EuZ}s«&OHErZOEHwS+¬~Owk }rWO sw¯
qs^t_ZrWOsv$ ¶}_ utWrZq~^v °J±Q?_ZEwX s v s¶}_uotZrWqss~Ov R~Owkqw}rW^Ew u]rW^EHwqrWEuZ}«
ro®h rZvw+OqrO}wk wk ° Mr¬+wXWwkqH~^wqrZ]uW}s« }rW s&&wXqsv ro®(}rZHqrZEv$wX utZwX uoE'~^ }rZ
}Xuo]w5^qrW]rWqsrW]ujr&s~Ow TXwro®hs~OwH sqOOsw}rWv$OOurZ°dÅ^rWqw^uovOwWZîh¬+w}rWO s¶HwXq
¶uqstWw¯Q m}kuwH sqO^wÆ H swXv$ Á®´qrZv.^qwXHrWO &}rZO ¶HwXqusrZO &~^w}rHrWqHEusw4uoOOqsrduW}s~Æ
OrZ OqmuZ}¶}XuoOwW°jzs~Ow' muv$wv$wWOî"s~OwHOv&]wXq|r®"OqsrO}wX swX ']}qwuo wX Js~Ow'OqrZEuOQro®
s~OwwXZwXH_o®nuOqswr®uOqsrO}wX X_¾uoE?_HHrWv$OrwÄjw}6_}rWO¶']wOrrZOtWwXq+OwXtZtZOwW°J¿~d^ Z~Ow
O]}rHrWqm]uwJuoOOqsrduW}s~wXO sOqOtrWvOro¯´®³qwXwX^wX + wXwkv r']w5s~Ow vrZqw5uoOOqsrWOqsuow|rWOw r
}rZEw¬s~uoqtZw¯n }XuwH sqOOsw$ H swXv J°
¿~^ 'EuoEwXq&HwkEH &r%^qrH¶Hwu tWwX^wXqmuo®´quvwk¬"rZq« ®´rWq'dsqO s}$uEuod s ro®5EuZ}«H¬uq
qsw}rWwkq¬~OwX}rZO ¶HwXqsOt}s~Ow}s«HErZHs u qwJ}rWwXqs]rWH J°OÅqs ^¬"w6®´rO}O rZs~Ow}rW]}wXOro®
}rZO swXH5}s~OwJ}«H]rWH uoEuZOHqwk Wwkq}kuqw®´O&~OwXq}rW^ swXE} sOwX ^¬~O¶}s~uqsw5}wkdsqmuo
]uW}s«H¬uoqm$qw}rWwXqswJ}~^O¶¹W^wX °^z~O +wXEj^+ " s~Or¬~EuoH¬~Owk uZ,+;,4@!? /
uo rO}¶uow¬~v$wX utWwk Xs~Ow+ wXUr®OrO}XuH}s~Ow}s«HErZHs ®³qrWvЬ~^}s~uqswX ^vw}rWv^OmuorW}Xuo
]w5}rZO swXH&qswX uqsw wX^uoqtZwj°Z¿~O "wuZH rqwXH +~Ow|OrWsrZO ro® ,-J'uE(!$ Q
v$wX utWwk H4}rW^ ¶HwXqs^t4~^w swXvuoH¶}$r®5v$wX utZwX (RnHwÀEOw`u&s~OwuOO¶}XuorWÆwkWwXS&u]
uZOHrW]u]OEHwXqsdOt'vwJ}~]uO v$ uJWu¶uOwrW}s~EuO^wX R´vOwXv$wXHw'u+~^w5 sH wkv wkWwXSX°
HwJ}rWEÁW¬+w"^qrWwu|~OwkrWqwkv RnuZ}]uuOwJ}wX uqsuE }wkd+}rWEsrWSÁrHwXswXqv$^w"î²uo
uoqOquqs swXr®}s~Ow}s«HErZHs " "}rZO swXHHs~O "}rZEHrW& ZwXq'tWwkOwXqmuou "uor¬ UsruW}X}wXO
rZq&r4HwXHÆrWq^~EuÆrWq&v s Otv$wX utWwk &Lu%}rW^ swXH wk&r®5rO}Xuo}~^w}s«d]rWH J°ÅOOqs~Owkq
¬+wtWZw5Q¬+r'HswXqwX sOt}rWqsrW¶uqwX rZO w®³Oh}s~Ow}s«H]rWH ]rZOw¬EOqsrHw5s~OwEuo ¶} srdrZ]®´rWq
HwÀEOOt$®´rWqsvuo'~Ow&HrZvOr'wIJwJ}u]~Ow'rWs~OwXq rW^w¬tZZwu& svOw vwXs~OrO$rrWOu
HrZvOro¯´®´qswXwqrZ]uW}s«&qw}rWwXqs}s~Ow}s«HErZdsOtutWrZq~^v °o¿~O ®´quv$wX¬"rZq«'O¶uJH u«WwX$qrZw|
Hwk tWOOt O]}rHrWqm]uwJHrZvOro¯´®´qswXw}s~Ow}s«HErZHs^t5utZrWqs~Ov ]~EuoUmu«ZwX u UwX }s~Ow}s«H]rWH
uo 5]rW s Ow&uE¸wÀEOOtw }wXH qwJ}rWwXqs sqmuowXtZwk ~Ow'OqswX wX]}wro®"ErZOEHwJ¸HrZvOr
wÄjw}J°
¿~^w&Eu]wXq sqE}sOqwJ4Hr$ÀEZw&vuo sw}rZO °Hw}srW4$Oqwk wXH &s~Ow&vrOHwkhro®6uo HH¯
}s~OqsrWOrZO sqs^Ow'wwJ}OrZO uoE'HqrOH]}wX +~Ow }rWE}wXO+r®}~^w}s«d]rWHHwXqsWuQ°HwJ}rW 7
HWwX stduowX '~^rWqrZOtW~^ OqrZOwXv qwkuowÂrs~Ow&OqswX wX]}wr®rZqO~]u4u]ºv s^tvwk muotWwX
½u qwX sOvwÆ}rWv$OOurZj ~^r¬^t~Owkq'EOwkE}wrW%s~OwHwÀEOsrZ%r®tZrZEu+}~^w}s«d]rWH
}rZO swXE}d°H±QHwJ}rWZWEWu~OwXrZqwXv rHwkwXqsvOwîÁuouqsOqmuoq' wX+r®h}s~OwJ}«H]rWH + "}rW^ Q¯
swXHuEQ¬"r&}rWqsrW¶uqswk rW$O w®³OrO}Xuj}s~Ow}s«HErZds uqswHqrOH]}wj° Hw}srZErZds "rZO+~Ow
v$rwX^t5ro®²s~Ow5rWvOr|wÄjw}°]ÅR]udJHw}srW^JÀEqs +~Ow|¬"wXïQ«d^r¬¾6O swXnÏ utWrZq~^v
Fx@[H &HwX }q]wL4rZOq}rWHswOuEÂ~OwXL srWvw&w^uovOwX 'r®^E}rHrWqHEuswL}~^w}s«d]rWHOt
uotZrWqss~Ov ~EuowXO ^qwHrZvOro¯´®´qswXwqsw}rZwXquqsw ~Or¬°
=>R/
"!#$
z7H sqO^wÆ}rWv$OOmuorW4}rWO s s &ro®5uÀE^sw swX&% ro®('LOqrO}wk wk )*%+-,.%0/*,2121-1,.%#354s~Eu
}rZvv&O^}kuw uE HE}s~OqrZO TXw'rWOH$wE}~]uOtZ^tvwk muotWwX J°6%wuo sOvw ~]uwJuW}s~¸rZqmHwkqw
Euoqro®Oqsr}wX swX ¸ }rZOOw}sw`H\u`u HE}s~OqsrWOrZO qswXuoOw¸u]\Hqsw}wJ`rZtW¶}Xuo5}s~Eu^OwX
¬~OrZ w$qmuoO v$ rZ<HwkuJH &uqsw&OOOqswH¶}muoOwO^ÀE^swW°<uW}s~4^qrO}wX s &qOO 'rW4u OqrO}wX s rZq
uoE'OqrO}wk rZq Hr OrW~]uJWwu s~Euqsw&v$wXvrZqHX~^wXqw| Or]rWOE®³rWqs~OwXqqwkuoWw sEwkwH u]
s~OwX$®nujuW}X}rWqm^t&r&~^w®Quïn srW$vrOHwXFxWxXH°
zLOqsrO}wX }XuowOw}Ow|HswXqEuoQ swXE&uoEwXZwXq muowXv$wXH J°z|&dswXq]uH uwkvwXHHrHwX
OrZ&dZrWWw}rWv$v&OO¶}XuorW°563~^wX7%8wOw}OswX uº wXE muowXv$wXH(@9X!:P6;%5<¸uZ}Euo
'OO &s~OwvwX s muotWw&=AHrs~Ow}~]uOOwk+®´qrZv>%#8r?%5<H°063~OwX@%8 wOw}OwX $~Ow smuswXvwkd
1;D,4A9X! :o+ OrO}s«WwLsuowu srWOwºvwX s muotWwPRQHqw}sw`r7%#8/S$~Euo uoqqsZw +~^wX u
v$wX utWw| ¬s~EHquJ¬&®´qsrWv rWOw ro®s OOO}s~EuO^wXuEHwkZwXqwr&%#8°<ROw}OrW^ r®h swXE
uoEHwXWwXqs uswXvwXHs uqw v$rwXw&H swXEuoEwXZwXq$wXWwkds °
p(qrO}wX s wX r®"u'H sqOOsw}rZvOOusrZuqsw@CB0-/ÃHrZ~Owkq¬"rZqmH JOwuZ}~OqsrO}wX Oqsr¯
H]}wX u @CB0'ro®5wXZwXH °+¿~O ' w¹ZOwkE}wºr®5wkWwXH $ ¾}XuowJ4s~OwG 6,4r®D% 8 uEÆ'
HwkOrWsw$dFE 8GIH2J8 H +
8
121-1 H2K8 ,21-121ê¬~Owkqw H-K8 L¯Q~wkWwXH+wOw}Osw$dF% 8 RH-J8 +u|À²}ssrWO wkWwXH
s~Eu&O¶uo TXwk D% 8 Ï rO}Xu smuow@Sk°"ÎjwkME K8 HwkOrWsws~Ow(,-/ 6,4r®N% 8 +~Ow$wXWwXH H2K8
E K8 G7H2J8 H +
8
121-1H-K8 u'^qwÀOro®OE 8 °<UZwXH |rO}Xuojr&u'OqrO}wk uqsw5srWu&rWqmwXqwÁ°Mr¬+wXZwXq^~Ow
swXr®huo^~Ow|wXWwXHs r®~^w5}rZvOOusrZ "rZOEuoq¶uorZqmHwkqwj°]ÎjwXQP.R _HwX^rWw s~OwY01@
",++1"+)R6'C"+TS+.>@,+XSEuoqsuojrWqHwXq5wÀEOw u +®´rZr¬ LRFêHS
U$ÈVXWZY³¥2Y´Ì5W\[^]`_ H2K8 R Hba< >Z 4?>dc
eAfhg Gji Nk G Ll xO ,
mAfhgn
Gji H-K
8
& @Q ;D&->N!?'+@DQ= Hoa
<
*&$C;,4 ; >=(O ,
pAf /,N* P;D Hoqr 0Z/5 H-K
8 R HbqrstHbqr R Hba
< f
ÎÁwX(u Ews~Ow' wX r®"uoR~OwwXWwXHs 5^qrOHE}wJºduH sqO^w}rWv^OmuorWHs~O 5}rZvO¯
urZ +vrOHwXwH&~Ow]uqs¶ujrWqHwXqwvu G Rxu;,CRBSX°HÎjwX H EwuowkWwXHr®yvu H~^w 01@5
ro® H s~Ow O^ wX|r®&vu E}E^t¾uojwkWwXH Hoz E}s~~]u Hbz R H °
V rWqwkrWwXqJ¬+w}rWO s¶HwXqs~EuROqrO}wX s wX +wOw}^w^qrWtZqmuov j¬~O¶}s~}Xuo~EuJZw"^rWH¯HwXswXqv$^ s¶}
smuswXvwkds ER´Q°wW°OqrO}wX s wX JÏH~O srWqwX U}Xu^OrWREw+wXHqwk OqswH¶}swH OqsrWtWquv$ j~OwX sw"^qrO}wX s wX
wOw}Ow@Sk°dÎÁwXUO ^rWw+~]us~O OqsrO}wX JÏ Ewk~EuJHrZqE}EwX JOOR OrZvw6r]s~OwE/A @
16,!J /6rW^wOqswX wkdsw% Fx57H"¬~OwXqsw&~Ow'rWO}XuoO w&ro®"OrW¯ÑHwkwXqsvO v 5Ow&r$~Ow
O^Oqw}mu^Qro®hv$wX utWw|quO sv srZHwkuJH J°
1 C0 i
i 0
i 2i
i 5
i
6 7i C2
i 8i i
C1 4 i i 3 0
S 0k
1
0 2
2
0 C1 C
j j P
P
Local State
Checkpoint Interval
Event j
k k
k C C
C P
i
Checkpoint j
C
k
m(-,-)
ÅRtWOqsw&x<REuv$Owro®(u&H sqOOsw}rWv$OOurZ°
X$ !0$ $X O!
[^][^]`_ UÈO¨Ì5YWR¥ü¤
ÎÁwX J
8
Ew&s~OwOsuo smusw&r®"^qrO}wX s M%#8°j¿~^wwXZwXH H-K
8
vrZwX (%#8®´qrZv ~Ow&rO}XuU smusw K
+
8
sr~Ow'rO}Xu smuow K
8
°j¿~^wrO}Xu muow K8
}rWqsqwX sErZEH 'r~^w&rO}Xuo~O srWqsE K8
jH¸wÀEOrZ
H
8
.Q@N6 K
8
î g G i uoEILZ°jÅRtZOqw$x ~Or¬ u&H qsOOwJ¸}rZvO^musrW~^wO ]u
sEuW}w¯nsv$wH¶uotWqmuov ¬~OwXqw rO}Xuo uwk &r®5^qrO}wX s wX uqswHwXO¶}swÆdÆqw}mu^tWO¶uq']rJwk °z
Q1.+ 656+ u' swXro®hrO}Xuj smuswX rZOw|®´rWqwJuW}s~OqrO}wX s °
z 5+ '! urO}Xuo" smuswro®6u^qrO}wX s
+
uoEº~Ow$ wX'r®5uor}ku"}s~Ow}s«H]rWH
u sOO swXro®6uohrO}Xuo uwk °063~Owk~OwXq&u$r}ku smusw rWq^rWu$rO}Xu"}s~OwJ}«H]rWHHrHwX 'OrW
HwkEwX]LrWÆ~Ow}rWv$OOmuorW%s wXî U}s~Ow}s«HErZHs uqwHwXswXqv$^wÆd%uÆOEHwkqH^t¸OqsrWsr}rW
¬~O¶}s~% ^EwXqsv]rW wJºrWº~Ow}rZvO^musrW Fê5H°]±Q%~^w'®´rWr¬Ot&¬"w}rWO swXq¾uH sqO^w
}rZvO^musrWvu uoE4uº swXro®rO}Xuo}~^w}s«d]rWH #"
v
$
HwÀEOwLrZ u%°% v K
8
qwX^qwX swXH s~Ow;L¯Q~
}s~Ow}s«H]rWHmu«ZwXH'OqrO}wk (%#8UuE$}rWqsqwX sErZEH sr rZvwrO}Xu] usw& 8
¬~&L&'R°dÅRtW^qwx
s~Or¬ u}rWqsqwX sErZEHwXE}w]wXQ¬+wXwXr}kuO smuswX u]&}~^w}s«d]rWH +r®^qrO}wX s %8°6%wu sOvws~Eu
wuZ}s~OqrO}wk u«ZwX 5uoO¶uj}s~Ow}s«HErZd( J
8
O}rZqqswX ]rWE^tr J
8
H¬~OwX + uqs °
)
ùjåjå¶ñWîRàãdîÑánäkå¶æèàôWäéXéèî&*XîÑéüäéèàJ÷äé÷³ñWî÷³âJãdàæêôåZæèìjäUéèàJ÷äéWì³å´äkå´îjåçñWäXå^ñWäXìOðHîîÑôì´å³àáQîïæêôì´å³äðéèîì³å³àánäkõXî+*óEîUì³äë
XäãáQà÷sîì³ìOñWäXìjå³äâîÑôä+éèà÷säéW÷³ñWî÷³âJãdàæêôüå
[^][^][ UÈO¨Ì5YWR¥oW¥JÈH¦H§ n¤
6 OtuouO sqmuZ}rZwXWwkEHwÀE^w$drO}Xuo²}s~OwJ}«H]rWH Jduod'Q¬+r5 sE}X}wk Zwr}kuE}s~Ow}s«H]rWH
K
8
u]
K
+
8
ro®²OqsrO}wX %#8hHwÀEOwu&HwkqWuQ°26%w}Xu ''+6,;D
K
8
s~Ow wX+r®jwXZwXH
OqsrOHE}w H&OqrO}wk d%#8h]wXQ¬+wXwX
K
8
uoE
K
+
8
R³]}EHOt'~OwwkWwXH~]uOqsrE}ws~OwrO}Xu
smusw}rZqqwk ]rWEHOt$r
K
8
Sk°Oz uowEuv^wZdÅRtWOqsw&x5HwkO¶} |~OwHwkqWu
Jr
°
)+!)9 |& 9U>0)' 8':)'\ +!#%
?!w!Z #
·+rZO ¶HwXq sqs^Ow$}rWv$OOurZO r®hutWZwXH sqOOsw&OqsrWtZqmuvº¬~O¶}s~'®nuoïQ srW&wXZwXH
}Xuo&rO}X}OqJ° H]}~&u&wkWwXHU "u }rWO sw¹ZOwXE}wr®u| H swXv}qmuo ~&v^w|HuowXqsqrZq¾u6®nuoïQ srW
OqsrO}wX srWqrZ¬~O¶}s~u|OqrO}wk q^O °W6w}Xuo^~EuoZ¬~OwXu'wXqsqrWq+rO}X}Oqs "&u6®nuïn srZOqsrO}wX srWqJ
~EuoswuoE~^w¾}rZHwXH r®"s WrZ¶uw srWqmuotWw' rW s°O¿Ur$rWwXqusw sE}s~®nuoO J .C'DAE,+
,,+,L,+;,4}ku&]w5u^OwJj°±Q&~^w5}Xuo wro®h}s~Ow}s«HErZHs^tEs~O "sw}s~OO¶¹ZOwqsw®´wXqs "srqwX srZqOt
OqsrO}wX swX r®u H sqOOsw&}rWv$OOurZr OqswXHrZO "}s~Ow}s«H]rWHw'rO}Xu^ muowX JW uJWwrW& smuoOw
srWqutZwWZ®´qrZv ¬~O¶}~$~O "}rWv^OmuorW&}Xu$Ew|qwX sOvwJ&wuW^tr&u}rZO swXHtWrW]uO smuswro®
s~OwqswX uqswº}rWv$OOurZHOrW^w}wX s muqs w¹ZOWuwXHr$~Ow ®Quw&rZOw?R´wZ°t]°Oî~OwOqrZtWqmuov
~Euo OrW¯ÑHwkwXqsvO s}| smuswXvwkds +Sk°
X$ @ X!
d$"
z Q1.+ & HwÀEOw3uo u swXro®5rO}Xu}s~OwJ}«H]rWH JrW^w®³rWq'wuW}s~LOqrO}wk °ÎÁwX&O
OrZws~EuuºtWrW]u}s~Ow}s«HErZd}rW^ sOwX uÂtWrWEuo uw r®~Owº}rWv$OOmuorWR°U±Q½tZwXOwXquQ
HÃÄjwXqwkd tZrZEuj}s~Ow}s«HErZds 5uoqwuJWuo¶uoOwW°W±Qs~Ow}rZdswOro®hqwJ}rWwXqsd]¬+wuqwrWO&HwXqswX sw
6NQ C.L'XU¬~OrW swOqsw} wHwÀEOrW%^wXwH &srdsqrOHE}ws~Ow^rWrZ¸ro®
qswX Ov$w}rWv$OOurZu]&~^w}rW]}wXO|r®hrZqO~]uuE$v$ s Otv$wX utZwX °
!0 x !Z$@ # X!#X$
±Q&rZqmHwXqruWOqwX s vrZqwOqsw} wk&s~Ow+ s Owro®²tZrWEuo}s~OwJ}«H]rWH}rWO s wkE}HWwX^ hHqsrOHE}w
srWvw+wkqv J°¿~Ow}rZvO^musrW&¬~O¶}s~¾u5®nuïn srZwXWwkd+rO}X}Oqs "¬HEw}kuw'~Ow >50]-4! S
"0C65-/ H~O "}rWv^OmuorW' srWO +u tWrW]uH uwZ°H¿~OwEuZ}s«d¬uq'qw}rWwXqswJ}~^O¶¹W^wvOwX
s~Eu Oqsr}wX swX uqswqsrWwEuZ}« rr}ku}s~Ow}s«HErZHs ®´rWqsvOt&u}rWO s wkdtWrWEuoh}s~Ow}s«H]rWH°
¿~Ow&}rZvOOusrZ]}EHOtuowXZwXH OqrOH]}wºs~O tWrWEuoh}s~Ow}s«H]rWH5^^ wXZwXH Oqsr¯
H]}wuJ®´swXqqwk Ov$OrW'®³qrWv s~O "tZrZEu]}~^w}s«d]rWH}rZO ssOw s~Ow,0!Y?!:0165-/^°Hz
uow^uovOwÅRtWOqsw' ~Or¬ u'H sqOOsw}rZvOOusrZJ®´rZqv$w&H&Q¬+rOqsrO}wX swX Á~Euo rZO
&~^wtWrWEuoO uswh) !
8 , !"
<
4uE'qsrW UEuW}s«'rs~Ow5}rZO swXH+tWrWEuoO}~^w}s«d]rWH) K
8 , a
<
4®´qsrWv
¬~O¶}s~~OwqwX sOvw}rZvO^musrW}XuoqswX uqs°
Pi
Faulty computation Pj
s Ci
C jt zj
i w
Resumed computation
ÅRtZOqw ]ÅEuoOQ¾uoEwX sOvw$·+rWv$OOmuorWR°
!0$ !0$ $ # !X#
]#]`_ ¦ U§W %ÈO¤J¤X§]ÈO¤
6ErZ~^wrO}X}OqsqwX]}wr®hu5®nuOqwZwXO + O^ErZ w(%#8UuEF%5< ]wqwk muoqsw®´qrZv }s~Ow}s«HErZds ! K
8
uoE a
<
qwk ]w}ZwXd°
U$ÈVXWZY³¥2Y´Ì5W ]`_ !Y'DQh= @).4d% 8 Q% < +rZqO~Euo A ,- 6/,+1,+
,?-> 5+' 9 K8 , a
<
:(>*/C;D,4 ;).Q@$6 a
<
A N*/N@Q ;D
1@'D .Q6 K
8 f
z|wEuv^w|r®rWqsO~Euov$wX utZw5 s~Or¬ÅtZOqwN7O°êu^°H¬~OwX¸}rZO ¶HwkqOt&L H 'JR =ZS n
K
8
uoE Hg H Rx= S a
< ° 63~^wX%~Ow}rWv^OmuorWqswX uqs '®´qsrWv K
8
uoE a
<
uZ}X}rZqmHOtsr~Ow
OrZH¯HwXwkqvO s¶}|EwX~]uJdrZq"ro®O%#8Q¬+r¾}Xuo wX uqswErZ s^w
*S /?; L H 'JRx= S? $,+ S+C016+Z $,+'0!Y(!:01D ]~^wv$wX utWwQ= HwXï
WwXqsw%Q¬+rvwk rw% < uJÄjw}Ot ~OwX@% < Ï rO}Xu smuow&Q¬¶}wW°Mr¬+wXWwkqjî~Ow&v&Os^w
HwXWwXqs4ro®(="uos~OwuO^¶}XuorW%wXZwXQHrHwX &OrZuJÄjw}&% < Ï }rWqqsw}sOwX PFêHrWq&îmUu
~Ow sd swXv wXZwXQduouWOHsrZEu^OEHwXqsdOt&v$w}s~Eu^ svH m}XuoqmHOt&HOO¶}Xuow$vwk muotWwX
uJWu¶uOw F]7H~Owk%~Ow$vwX s mutZwM= rZqO~]u%¬~%qswX ]w}&srPR K
8 , a
<
SXR¬UOrrZOtWwXq
qwXvurWqsO~Eu ¬s~qwX sEw}r$rWqmwXqwº]uq ro®}s~Ow}s«HErZHs R
8 , <
S6¬~ L'u]
k6uo s~Ow qwX sOvw}rZvO^musrW&= ~]u ]wXwX swXHrWE}w'uE$qwJ}wXWw rWE}w
*S /N;DZL
H
'JRx= S 5 ,+ S+0C6$Z/:,+''0!??+!&"01D/ Z~OwX$~Ow|vwX s muotWw=
qwXvuO HwÀE^swXrZqO~Euo°
±Q srWvw}Xuo wX s~Ow¾uoOO¶}XusrW}kusrWwXqmuowrZqO~]uvwX s muotWwX $FH°"<UWwX ~OrZOtW~s~OwuoOOï
}XuorWLHrHwX &OrZrZwkqmuswrWq^~EuO Ju ' wXwk uoErZwWR¬~OwX4s~Ow H swXv }XuÆqw}rZwXq'®´qsrWv E}s~
v$wX utWwk ~OwX}Xu$Ew v$rWvwkduqs rZwXqmuow$ E}w5s~OwX$¬]Or'rZOtWwkq"qswXvuo&rZqO~]u$~Ow
®´^OqswW°
C jt s
Ci
C jt
s Ci
delivery j send
m Pi
Pj
Pi
P send
m
delivery
(a) the message m is orphan (b) the message m is missing
ÅRtZOqwN7 |qO~]uuE(V s Ot'vwX s mutZwX °
]#][ Yn¤J¤oYW %ÈO¤¤k§]ÈO¤
6ErZ~^wrO}X}OqsqwX]}wr®hu5®nuOqwZwXO + O^ErZ w(% 8 uEF% < ]wqwk muoqsw®´qrZv }s~Ow}s«HErZds ! K
8
uoE a
<
qwk ]w}ZwXd°
U$ÈVXWZY³¥2Y´Ì5W ][ !Y'DQ= @&.4d%8 % <( v$ s Ot(A ,+'-' Y/,+1,+
, > @E+' 9 K
8 , a
< : >? @Q ;3.Q@?6 K
8
/ C;D,4 ;D
1@'D .Q6 a
< f
z|ÐwEuv$Owr®&v sOt4v$wX utWw% s~Or¬Ð ÅRtW^qw 7O°°6¬~OwXqw@L
H
'JR =ZS
K
8
u]
H
g H
R =ZS n
a
<
°563~Owk¸s~Ow}rWv$OOurZqswX uqs ®´qrZv
K
8
u]
a
<
uZ}X}rZqmHOtrs~Ow^rWH¯
HwkwXqsvO s}|]wX~EuJHrWq+r®%#8UQ¬"r&}Xu swX uqsw5]rW s Ow
SZ/(; H
g
H R=ZSG ,+ S+C016 /Z,+''0!? !:01D U%rWqHwXq'~Euo~^
qw¯QwOw}^rW%]w®³wu s^wZEs~Ow&vwk muotWwD= RQu wX]HOt |OrW qsw¯nwwJ}OwJS~]u r$Ew
qw}rWqmwÆdº~^w& H swXv¼wXWwk"rZqrWtWtZwº rZvwX¬~^wXqw&rZ%OrWH¯}rZqq^Ow srWqmuotWwW°R±³®~^
qw}rWqm^t~Euo OrW+EwkwX¸HrZOw~^w5v$wX utZwN=qswXvuoO "v$ Ot
S /; Hg H Rx= S? 5L,+ S+0C6$Z/N,0!?+?!&"0C65-/ H~Owk =qswXvuoO
v sOt ®´rZqwXZwXq°
z| "^qwXHrWO sd$ rWv$w}ku wk ~Owu^O}kurZ¾}XuosrWwXqmuow|v s^t5v$wX utZwX °<UWwk~^rWOtZ~
s~OwuOO¶}XuorW&HrHwX +OrWsrWwXquw|v sOtW J¬~OwX$~Ow| H swXv}XuoqwJ}rWwXq+®³qrWv sE}s~vwk muotWwX
R³d}rW^ ¶HwXqs^t& muowX ro®(}s~EuoOOwX NFx7OW]jxH/Sv$ OtZ "}Xuo]w vrZvwXHmuoq rWwXqusw$ E}w
s~OwX¬]Or&rW^tWwXq+qwXvuv$ Ot$~Ow®´O^qwW°
@$! $ X$ "#$!! X! dX$X
z|4rWqHwXqswÆEuqZR K
8 , a
<
S }rZO swXH&î5uvwk muotWwX ' wkd&H?% 8 r?% < % K8 ~EuJZw]wXwX
HwkZwXqw r@%5<¸]w®´rZqw a
<
°"¿~^wOqwkdrZO H m}O s rW Rn}Xuo wX QQÃnS ~Or¬ ~]u3 rZvw
}q}Ov smuoE}wX Jj E}s~%u&EuoqR K
8 , a
<
S }rZO¶]w}rW^ ¶HwXqsw%}rW^ swXH5wkWwXº~OrZOtW~ E}]HwX
swXEHOt'wXWwkds r®v$wX utZwX "u]OrZ~^w5}rZqqwk ]rWEHOt&HwXWwkqwXZwXH +rWqH¶}wZwXq uO°Z¿hr'ur¬
sE}s~%ErZ OwX JEv$wX utZwX uqswutZtWwºuE ~^w'®´rWqsvuUHwÀE^srWro®6}rZO swXE}%mu«ZwX E}s~
utW +HruW}X}rWOH°O»6wO HO^ w}srWO HqsrE}wutZtWOt r®v$wX utWwk "uE&}rWO s swX]}ro®tWrWEuo
}s~Ow}s«H]rWH °
]^]`_ § 5YW ºÌ %ÈO¤J¤X§]ÈO¤
z DQ& &u s rO}¶uswƬ~%wuZ}~Lv$wX utWw EH¶}XuowX &îs~Owv$wX utWw}XuÆEw$rWqsO~EuLuErWq
v$ s Ot¬~%qswX ]w}&srEuqs r®rO}Xu+}~^w}s«d]rWH J° <uW}s~ÆvwX s mutZw& muotWtWwJº¬s~4uEuoq ro®
utW H =HwuZHOtsr®³rWOqHÃIJwkqwXH usO ,-JG,!*+Qü ,-J .01L5L!$ 'Qü
!$ Q .0C "5 ,-J^N /,G,-J ", !$ Q°"¿~HO J®´rWOq&]u ¶} QHEwX ro®v$wX utZw
HwkZwXqwX uqw ]rW s Ow
# CC' 4 v$wX utWw&HwXWwkqPR³vwX s mutZwX uqswutWtZw Rd,&SkjQ°wZ°]v$wX utWwk }kuOOrZ Ew
wX~OwkqrWqsO~EuorZqv sOt Sk
: 5 vwX s mutZwHwXWwXqs R³vwX s muotWwX uoqw$mutZtWw R ,&SXRn°wW°jv$wX utZwX }Xuo%Ew
rWqsO~EuO^OrWv$ s OtSX
:&!YD)|vwk muotWwwXZwXqGR³vwX s mutZwX uqswmuotWtWwJPRN, = SkjQ°wW°HvwX s mutZwX }Xu Ew
v sOtOO^rWrWqsO~EuoSX
$-,+OrW'vwX s muotWwHwXWwXqs?R´v$wX utWwk (uoqwutWtZwR , = SkWQ°wW°Xv$wX utZwX "}Xuo
EwwX~OwXqv$ OtrWqrWqsO~EuoSX°
¿uotW }XuoEw+ wkhwks~OwXqUH ~OwuO^¶}XuorW| wkè®Hu}rZvOwXqjrWqRH5s~Ow+OEHwXqsdOt| H swXv
¤k¥§^¥-YQ¨&¥J§ YW "uÂvwX s mutZwWs~Eu®´rWq$~Ow%u^O}kurZÏ swXvuods¶}}ku`EwrZqO~]u+¬Ew
muotWtWwJ d%s~OwuO^¶}XuorW%rZqH%s~Ow}rWv$Owkq°·+rZO w¹ZOwkdsdUî~^ 'vwk muotWw$
rWqsO~Eu¬~qswX ]w} r&u'Euoq+r®"}s~Ow}s«H]rWH ^vuJqswXvuo$rWqsO~Eus~Ow ®´^OqswW°
ÍRÉ WU§ ?YQ¨&¥J§ 5YW Eî"s~Ow' H swXv7vuHmuO +H®´rZqvuorWu]rWO|~Ow']wX~EuJHrWqro®"~^w¾uoOOï
}XusrWGR´wW°t]°EHwXswXqv$O ¶}^Ow}wX¬ sw¾HwkwXqsvO s}|rZqOrZH¯ÑwXwXqsvO s¶}SuE$ uoOw
r¸ }Xuq%HOO¶}XuowX Js~OwX%~^w& H swXv }Xuo%mutv$wX utWwk u wXO sOqwX &s~OwXº¬
qwXvu^rrW^tWwXqrZqO~EuoO ~Ow|®´OsOqwZ°
¿~^w uvwH }O srWº~OrW¶H |®´rZqmuotWtZ^t&vwX s mutZwX u |v s^t(R'5. !)Sk°E±Qº~^w®´rZr¬Ot'¬+w
uo ^vws~Eu&u vwX s mutZw&muotWtWwJBRd,
@
S ¾uv$wX utZw~]u&}XuO^rW'EwrWqsO~Euo%OO&vuJ Ew
v$ s OtuoEs~EuuvwX s mutZwmuotWtZwPR
@
,&S u&vwk muotWw'~Euo}XuO^rW]w&v s Ot&OO|5vuJ
]wrWqsO~Euo°
]^][ 5Ì5W¤oYQ¤X¥JÈ W¨ÉºÌ § ´Ì]£U§ "¨UÈO¨Ì5YWR¥
¿~Ow%HwÀ]OrW3ro®~Ow%}rW^ swXE}`r®tWrZEu }~^w}s«d]rWHwk rWLutW uo rO}¶uow ¬~LwuW}s~
v$wX utWwZ°W¿~Owk w muotW "uor¬ÆrHqsrE}w5uqw EwZwqwkuorW&ro®wE}O rZdwXOrWsw
R`ZrW&rO}Xu