HAL Id: inria-00073712
https://hal.inria.fr/inria-00073712
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- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Specification and Verification of various Distributed Leader Election Algorithm for Unidirectional Ring
Networks
Hubert Garavel, Laurent Mounier
To cite this version:
Hubert Garavel, Laurent Mounier. Specification and Verification of various Distributed Leader Elec- tion Algorithm for Unidirectional Ring Networks. [Research Report] RR-2986, INRIA. 1996. �inria- 00073712�
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
Specification and Verification of various Distributed Leader Election Algorithms
for Unidirectional Ring Networks
Hubert Garavel, Laurent Mounier
N ˚ 2986
Septembre 1996
TH `EME 1
$ #%&'")(* ',+.-/102-!34576'89#
:4<;='!7/7!-?>@3BACDFEG7HI#
JKLNMPOQSRUTVOWTYXFMPZ\[P]^TVKO_MP`aQSbdcFK`efMPOWg
hDiaj
klmkmnpoBqSrkWstkWu:vxwIkystzxsty
j
k_l{kWs
|}~:
k!yYVk_!y } k
qu:
~ }
yxk
}
kW
i k } i
k: oBYk_xyk_l4
}
kn_ oBu k_s
I_: hDi
s } k
~ }
y{k_u: s¡
y i y i
k£¢
~}
lu:Ds¤kW
¦¥
u:y
§~
¨u *©k }ª¥
_u«y
¦~
~
¢p
sty }
vyk_¨¦kWu xk
}
k§k_y
¦~
Su ¦
~ }
y i ls/¢
~ }
umsk!y
~
¢lu i
k_s
~
k_yk_Yzu{v
§}
kWy
§~
¤u:
}
mky¬¡
~}F®
Pyu } y
¢
}~
l2u:¯u:§
~}
y i l<
}~
~
stkWUYz±°%k°²u
³n_Y´ ´xµ²u:
ys ©«u }
u:Py }~
~
sk_Pz¯¶
i
u:u
q ~
Vk
}
ys
n_P´:µ:¡/kpstyv¤xz{y i k
}~
vstykWss
~
¢ay i
s/! u ss
~
¢²u:§
~ }
y i ls
I
}
k_skk
~
¢%v
}
k_
u:¦k
~
lmlvx·
_u«y
¦~
SlmkW
vl¸u ¤¹
~}
v
}
k
u §k lmu
i
k_s
®º
k4stv kWs¬y©«u }§~
vs
lm
}~
© klmk_y5s
~
¢»y
i
kWstku ¦
~ }
y i ls
~ }
xk } y
~~
xy5u
Su¢¼v§§zI¢½u:vªy·fy
~
§k
}
u:Py
}~
y ~ ~ ®
hDi
k_sk'u:§
~ }
y i lsmu
}
kS¢
~ }
lmu ¦§z¨xkWs
}
Vk_?vs
±y
i
kU¾5¿WÀ.s¤kW
¦¥
u:y
§~
Á§u vu k'ÂÃÀ²Ä%ÀÅ¿Su Á© k }¦¥
k_
Æ¢
~ }
u ¥
wYkW±Pvl4Vk }~
¢Ãlu i
kWsÇvs
Sy
i
k'ÈÉÅʲË
Æ
ÈÌp¿É²Í²¹ ÎÏPÊ4Ð ÑÒ
ɲÍFÉÅÓVÇÔy
~Y~
§
~ w
®Õ'~
xk_ª·Ö
i
k_
Y
u:±
s
l4v§u:y
§~
±ykW
i
×
vk_su ¦
~
¡y
i
k© k }¦¥
u:y
§~
~
¢/y
i
kWstk
~
x·\y }
© u:u ¦
~ }
y i lsy
~
VkIu }}
kW
~
vxy
u:vxy
~
lu«y
_u:§¦z
®
Ø'ÙÚFÛÜ4Ý Þ» ß s
lv§u:y
§~
s_µpà
s¬y }
vxyk_.á§
~ }
y i ls_µpâ
~}
lu Ôàpk_s
}
xy
§~
h kW
i
×
vk_s_µâ
~ }
lmu
Õ
k!y i~
sµa°Åu:Vk§¦kW
h²}
u:s
y
§~
UYzxstykls_µV°²k_uxk }ã
§k_y
¦~
%µaÂÃÀ²ÄaÀ»¿µ Õ'~
xk_ª·Ö
i
k_
Y
µ
|}~
!k_ssá¦k
}
u s_µ
|}~
y ~ ~ ã
kk }
µYVk_
ª¥
_u«y
¦~
%µ hÅ~
k_q
¤µäu:
u«y
§~
²µxä7k }ª¥
_u«y
¦~
®
å æ{ç
èéëê_ì
ç
èí»î éëïfð!ñ
ò_óôõfö%÷!ø¬õ\ùfúûôüô5ýYö\óWúûù²õfø¬þ ôõ½ö%úûüÿ
è è ì»ð:êWî èì/ì
ù\þ:øtú úûù\ùøôü ü"!"ù½ö\õfú#$&%%ø'ûøÖ÷5üö)(»þWþ"ûú#'+*
öfúûôüù²ô5ý-,«ôõ.&/(»ü0$_ù\úûù1xøëóüWú#2ø¬ù
/3
5ü*4,«õ\úûùfô5»õ\ôô5öfø65ü7!98:5õföfúûü;%²ø.
ø!úöfôõ\ù
=<'>>?7@
A6B*4.&5ú#DC=EFGIHJK-LDMNJNOHPQ7RS"NT-LDUJ
V üõfú%²óXWôüWø*D(Yûþ:ø¬ù[Z6\¤øtõfú#.&]
8Ôúûüúûþ05õ^*_ úûõfùfö
õøa`X¬÷!ôúûù\úûø¬õ
,-*4bcbbd 8Ôôü!öe ôüWüô5öNò75úûü!ö*48:5õföfúûü
,«õf5ü"¬ø
@
Bg*4.&5ú#DC
h
N+FJH+iK-LkjlFi0R'HJQ7RS"NT-LDUJ
Unit´e de recherche INRIA Rhˆone-Alpes
655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN (France)
!#²»_&'"# -!/!{)#","' #Å")'" "''!7/'-
Ù Ù
¶Ãk
}
u:
~ }
yp
} rkWstk_yk u£s/rk_
ª¥
u«y
¦~
'k!yÔ§u©Nrk }¦¥
u:y
§~
S¢
~ }
lmk§¦kmu:§
~ }
y i lmk_sp
s¬y }
vDrkWs
¬rk§k_y
¦~
Ssv
}
v
} rk_sk_u vIk'u k_u vv
¦}
k_!y
§~
k_
®
á*u } y
¦}
vu:§
~ }
y i lmk7
}~
~ sxrk7u
}
°%k/°²u: kn_Y´ ´Ãky»xkNsu©«u }
u:Pyk7
}~
~ srk_k»¤u
} ¶ i
u:kyÅq
~
¤k
}
y5s
k£nWP´:µ
~ rkyv
k u }~
vstyk_sskNxkÃk!yykD! u sstkNu ¦
~ }
y i
lmk_s%k_4
} rkWstk_!kxkDu u:vwÔxkD
~
lml4v
u:y
§~
k!y¹
~ v xklu i
k_s£
~ ¥
u:§k_s
®~
vs£sv7rk }~
s
r
k }
k_Pyk_s£u:l¨rk
§~ }
u«y
§~
¤sxkk_s£u ¦
~ }
y i lmk_sIu
¥
~
xyk_
§}
v
}~
y ~ ~
¦k } rk_s
s¬y5u:Py
j
um!kWsu k_s
®
¶Ãk_s*u ¦
~ }
y i lmk_s
~
Py kyrr kÁ¢
~}
lmk§§klmkPy¨/rkW
}
y5s
j
u u
xk xv u:Pu:k³k stDrk_
ª¥
_u«y
¦~
GÂÃÀ²Ä%ÀÅ¿³
~ }
·
lmu
sxrk u
}
¾¿WÀ k!yU©Ãrk }¦¥
r
kWs Æ ~ v }
v ~ l4
} k ¥
wÃrk¯xk¯lu i
kWsÇ
}
u k
j
u? u³
~
yk
j
u ~ vy
§s±ÈɲÊÅË
Æ
ÈÌp¿É²Í²¹ ÎÏPÊ Ð ÑÒ
ɲÍFɲÓFÇ
®ã
vxy
su:PyÔxk_syk_
i
§×
vkWs¢
~
/rk_k_ssv
}
u7rkDrk } u«y
§~
£k!w
i
u:v¤s¬y
©kk!y§k_s
}
k_§u:·
y
§~
sÃxk
s
l4v§u:y
§~
%µ§u ©Ãrk }¦¥
_u«y
§~
mxkk_su ¦
~ }
y i lmk_s7
~
x·\y }
©
u:vxw¤k_vxy
ky
}
kDk
k_yvDrk_ku:vxy
~
lu«y
§×
vk·
l{k_Py
®
Ý W Û Ù
á§
j
k_
}
k_sDxk }~
!k_ssvsµá¦
~ }
y i lmk_s
sty }
vDrk_s_µ ß s
lv u«y
§~
¤sµ
ã
¦kWy
§~
²µÖ7rk
k }
kÔxkWs
}~
y ~ ~
¦kWsµaÂÃÀ²Ä%ÀÅ¿:µ Õ rky
i~
xkWs¢
~}
lmk_¦§k_s_µaqrk_sk_u v
j
u ky
~
%µ²qSrkWstkWu:v'k_u:k_u v%µ%YDrkW
¦¥
u:y
§~
%µ%Yzxsty
j
k_l{kWs
xkÔy
}
u:s
y
§~
s£rky
×
vk!yrkk_s_µ
h
kW
i
×
vk_sxkk_s
}
xy
¦~
£¢
~}
lmk_¦§k µxäu
u«y
¦~
%µxä'rk }ª¥
_u«y
¦~
®
< =
{7I"/
¤!kIy
i
k£kWu
}
¦z u«yyk_l{ys
~
¢u:vy
~
lu:y
I
}~
y ~ ~
éu
u:y
§~
*u }}
k_
~
vyYz¯¶
®»º
k_sty5>
º
kWs5´:!?ëµ¢
~ }
lmu
© k }¦¥
u:y
§~
£ k_k
}
u:\µYu:Iy
i
kÔs
~
·ë_u:§¦kWml
~
ka
i
k_
Y
u
}~
u
i
u } y
!v u } µ
s/s
~
lmk!y
lmk_sD
~
Py }~
·
© k } s
u @
A â }~
l.uDy i k
~}
ky
u
~
y
~
¢x©
k_¡ µy i
sÅ
}~
§kl u: VkÃ
~
s
xk
}
k_ us²s
~
§© k_p¢
~}²¥
ykÃstyu«ykNszYstyk_ls
s
¤!kÔ© k }¦¥
u:y
§~
Su:§
~ }
y i lsDu
}
kÔ
~ ¡ ¡/k§ª·
~
¡CB
A â }~
l¸u£u
© k
~
Py
~
¢©
k_¡ µ¤¢
~}
lu ²© k }¦¥
_u«y
§~
spvstk_¦kWss_µFs
!k
~£}
k_u
sty
u:
u:y
§~
U_u:'Vk
¢¼v§§z£© k }¦¥
kWaµu:£y i
s
}~
¦k_l
sDvPy
}
u y5u:§k u:YzY¡/uzVk__u:vsk
~
¢Åy
i
ks
ED
k ~ ¢ } kWu:
sty
Ôstzxstykls
®
â
~ }
yvu«yk§z µ
}
kWu:
y¬z
s4l
~ }
kIs
i
uxk_C@
}
u !y
u k!wxVk }
lmkPy5s4u:
}
k_u zs i~
¡ÃkWy
i
u:yy
i
kWstk£l{ky i~
s{u } k
~ ¡ u:
u:¦k
Uu
xvsty }
u Å
~
PykwPyWµau:Sy
i
u«yy
i
k_z'u:'
}~
©
xk4u:
lm
~ }
yu:Pyu
'y
i
k{xk_s
~
¢7u u
}
kÔ! u ss
~
¢u:
u:y
§~
s_µstv¤
i
us
sty }
vxykWstzxstykls
~}
~ lmlv
u«y
¦~
}~
y ~ ~
§s
®
hDi
s } k
~ }
y
§¦v¤s¬y
}
u:yk_spy
i
kIu:
u:y
§~
~
¢/styu:yk!·
~ ¢·\y
i
k!·Öu
}
yp© k }¦¥
_u«y
§~
lmk!y i~
sy
~
u£
~
x·\y }
© u:7ustk·
s¬yvxz µ i u }
x¦zy
}
u !yu ¦kSs
lm§z±Yz
i
vlu:
}
k_us
~
®
Py5u }y
¢
}~
l2y i k
~ }
u:Nk_s
}
xy
¦~
~
¢y¬¡
~
¢½u:l
~
vsu:§
~}
y i lms_µy
i k ~
k
}~
~
stkWYzGF
®
°²k°²u H>°²u V´ ´?u:¤
y5s©«u }
u:Pyp
}~
~ stkWPz
ã®
¶ i u
u:q
® q ~
Vk
}
ysI>¶/q´«!?ëµ
~ v }~
k_y
©k4¡Du sy
~
xk_s
UuI¢¼v¦§z'¢½u vªy·fy
~
§k
}
u:Py§k_uxk
}
k§k_!y
§~
u ¦
~ }
y i lµ
y ~ stVk_
¢¼z
yv¤s
my
i
k4ÂÃÀ²ÄaÀ»¿p u:vu:k µxu:£y
~ ¢
~}
lu ¦§z© k }
¢¼z
yvs
{y
i
kmÈɲʲˣy
~Y~
¦
~ w ®
hDi
s } k_
~}
y s
~}
Pu:
3D
kW?usm¢
~
§
~
¡s
®
xk_y
¦~
±
}
k_skPysmy
i
kÂ/À%Ä%À»¿S§u v¤u: k'u Yk_!y
§~
© kWs
u:
~
© k } ©
k_¡
~
¢Ãy
i
kÈÉÅʲËUy
~Y~
§
~ w
®mº
kmy
i
k_¯s¬yvxzUsk©k
}
u:© k } s
¦~
s
~
¢Ãy
i
k§k_uxk
}
k_¦kWy
§~
u:§
~}
y i l
vxk }
¤
}
k_u s
§z£sk© k
}
kp¢½u
§v
}
kussvlmxy
¦~
s@
}
k
u:§k
su
}
k_
u:§kÔlu i
k_s
Æ
YkWy
§~
5JYǵv
}
k·
u:§k
su:
}
k
u ¦klu
i
k_s
Æ
xk_y
¦~
HK ÇÔu aµ
¥
u:§§z µ»v
}
k
u ¦k
su: v
}
k_
u:¦klu i
kWs
Æ
YkWy
§~
'PÇ
®
L M
6ON489- $ #Å_!{
M
N6''P" (RQ
M
Q@
Õ
u:Yz'¢
~}
lu:
stls
i
u© k{Vkk }~
~ sk_¢
~ }
xkWs
}
u
}
u:§¦k_7stzxstykls_µ²u:l
~
¡
i
i µ²y
i
kstyu u } ·
D
k_ â
~ }
lmu 7àkWs
}
xy
§~
h k_
i
×
vk£ÂÃÀ²Ä%ÀÅ¿TS
i
u s
}
k_k
© kWUu
~
s
xk
}
u ¦ku:ytyk_Py
§~
¢
}~
l,y i k }
k_sk_u } i
~ lmlv
y¬z
®
ÂÃÀ²ÄaÀ»¿
s7u¢
~}
lu:x u: vu k
Pyk_xk_¢
~}
y i ks¤kW
¦¥
u:y
§~
~
¢V
~
lml4v
_u«y
§~
{
}~
y ~ ~
su:
sty }
vxykW
stzxstykls
®
ëyÔ¡Du s k© k_
~
¤kWUxv }
Sy
i
kzk_u
}
sn_nUx
±y
i
km¢
}
u:lmk_¡
~}~
¢Ãy
i
k£
ã
àWVÔ+X{
}~
k_!y u
s¬y5u:u }
ED
k_{Yzm¾¿WÀZY
'n_ [>tV 7?
®
Yk©k
}
u:xyvxy
~}
u: s¢
~}
ÂÃÀ²Ä%ÀÅ¿u
}
ku©u
u:¦kµ:k
® ® >
ßDß
µ h v }
!?
®
hDi
k4xkWs
~
¢Â/À%Ä%À»¿Ô¡Du sl
~ y
©u:ykWPzy
i
k4k_k_S¢
~ }
u u:vu:k¡
y i u i
i u:¤s¬y
}
uy
§~
§k©k²u 'u
s¬y }~
4lu«y
i
klu:y
u:Fus
s_µP¡
i
i ~
v§£¤kÔvsk_I¢
~ }
y i kÔxkWs
}
xy
§~
Su:u:u ¦zxs
s ~
¢»
~
lm§k!w£szxs¬ykls
®
ÂÃÀ²ÄaÀ»¿¢¼k_u:yv
}
k_s/y¬¡
~
!§k_u
}
§zIstk_u
}
u«yk_u
}
ysT@
\^] Ù ÞÅxW_»x ~
¢ÂÃÀ²ÄaÀ»¿
s/xkW
_u«yk_y
~ y i
k xk_s
}
xy
§~
~
¢Åu:yu4sty
}
v!yv
}
k_s
®
ëy
s/u sk_
~
Iy
i
kp¡/k§¦·
~
¡Sy i k
~ }
z ~
¢u:§ k
} u
Ôu:¤s¬y
}
uyu:yu{y¬zY¤kWsµ¤l
~ }
kstVk_
ª¥
_u:§¦z
~
Sy
i
k{Î'`¤Ä.aÓ Ñ s¤kW
¦¥
u:y
§~
u:vu:kI>
ãNÕ
7KPµ
Õ
q%äpPb?
®
Öy i
su
}~
u
i
µ%u«y5usty
}
vyv
}
k_s u
}
kmxk_s
}
Vk_±Yz
##
µ%¡
i
i } k_
}
kWstk_Py©«u:§vk
~
lmu
¤sµ²u
cd)#
µ¡
i
i u } klu«y
i
klu«y
_u:x¢¼vy
¦~
sNxk
¥
kW
~
{y
i
kWstkp
~
lu
s
®»hDi
klmk_u:
~ ¢ ~
¤k
}
u:·
y
¦~
s
sNxk
¥
k_mYz4u:§ k_
} u
e")#
®
~}
y5sµ
~
Vk
}
u«y
§~
¤sµ:u {k
×
vu«y
¦~
s7u
}
kD
}~
vVk_
ml
~
xv¦kWs
fg
!ê"!è1hji:ètì»ðkCh lè'
ÿ
ðWè m
î
n ÿ
Öî3o ½èqp«ï
«ìDè'«îîErWètsNèté
jhxð_è s
éëîD 3u
ê_îè,l ÿ/v
éëîètì/éf
BaòTw %)41'þõfôx½ø'Öözy
< d