• Aucun résultat trouvé

Validating fault-tolerant behaviors of synchronous system specifications by discrete controller synthesis

N/A
N/A
Protected

Academic year: 2022

Partager "Validating fault-tolerant behaviors of synchronous system specifications by discrete controller synthesis"

Copied!
7
0
0

Texte intégral

(1)

HAL Id: hal-00419542

https://hal.archives-ouvertes.fr/hal-00419542

Preprint submitted on 24 Sep 2009

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.

Validating fault-tolerant behaviors of synchronous system specifications by discrete controller synthesis

Emil Dumitrescu, Alain Girault, Eric Rutten

To cite this version:

Emil Dumitrescu, Alain Girault, Eric Rutten. Validating fault-tolerant behaviors of synchronous

system specifications by discrete controller synthesis. 2004. �hal-00419542�

(2)

!"#$ %&' (!%) &'* +, ! -

-!%$ .'/0.''./$ 1!%-#

23456785

9:;<=>?> <@A?=@BB>= ;CA?D>;:; :; E;>F ?@ G@=HIBBC I;J

;>;; ?D> GIEB?J?@B>=IA<> <IKIL:B:?:>; @G I F>K>AFILB>

;C;?>H G=@H ?D> >I=BC F>;:MA ;?IM>;N OIEB?J?@B>=IA<>

:;?D> IL:B:?C@G?D>;C;?>H ?@ DIAFB> GI:BE=>;;@ ?DI?

:?; ;>=P:<> IAFQ@= K>=G@=HIA<> :; HI:A?I:A>FN RE=

@=:M:AIB:?C :; ?@ E;> F:;<=>?> <@A?=@BB>= ;CA?D>;:; ?@

I<? @A IA >S><E?ILB> ;K><:T<I?:@A :A @=F>= ?@ C:>BF

I A>U GIEB?J?@B>=IA? >S><E?ILB> ;K><:T<I?:@AV K@;;:J

LBCA@AJF>?>=H:A:;?:<N WD>AVU>@L?I:AHIAEIBBC?D>

TAIBF:;?=:LE?>F:HKB>H>A?I?:@AIAFU>G@=HIBBCP>=J

:GC :? IMI:A;??D> :A:?:IB GIEB?J?@B>=IA? ;K><:T<I?:@AN

X YZ

56[\]85^[

Z

WD:; U@=_ IFF=>;;>; ?D> GIEB?J?@B>=IA<> :;;E> :A

F:;<=>?>J>P>A?;CA<D=@A@E;;C;?>H;F>;:MAN OIEB?@<J

<E==>A<> HE;? L> ?I_>A :A?@ I<<@EA? G=@H ?D> >I=BC

F>;:MA ;?IM>; @G F>K>AFILB> <@HKB>S ;C;?>H;N O:=;?V

?D> F>;:MA>= HE;? ?D:A_ IL@E? ?D> GEA<?:@AIB:?:>; @G

?D> ;C;?>H ?DI? HIC GI:BN WD>AV G@= >I<D K@;;:LB>

GI:BE=>V I ?@B>=IA<>K@B:<C HE;? L> ;K><:T>F :A @=F>=

?@ B:H:? >==@=K=@KIMI?:@A `IAFK=>P>A??D>GI:BE=>@G

@?D>=<@HK@A>A?;aIAF?@ >A;E=>?D><@==><?L>DIP:@=

@G ?D> ;C;?>HV F>;K:?> ?D> GI:BE=>N b? ?D> GEA<?:@AIB

B>P>BV I GIEB?J?@B>=IA<> K@B:<C :; F>;<=:L>F I; IA IFJ

F:?:@AIB L>DIP:@= ?DI? ;D@EBF L> >AILB>F UD>A>P>=I

GI:BE=>@<<E=;N c?;KE=K@;>:;?D>?@?IB @=KI=?:IB<@HJ

K>A;I?:@A @G ?D> B@;; @G GEA<?:@AIB:?CQK>=G@=HIA<>

?=:MM>=>FLC ?D> GI:BE=>N

d@U>P>=VM:P>A?D><@HKB>S:?C@GIA>S><E?ILB>F>J

;<=:K?:@AV K=@M=IHH:AM I GIEB?J?@B>=IA<> K@B:<C :; I

P>=C F:e<EB? ?I;_N cAF>>FV ?D> F>;:MA>= HE;? ?D:A_

@G IBB K@;;:LB> >P@BE?:@A; ?DI? HIC G@BB@U ?D> GI:BJ

E=>@GI <@HK@A>A?VIAFF:;?:AME:;D UD:<D@A>;HE;?

L> IP@:F>FN fE<D IA IKK=@I<D :; A@? =>IB:;?:<V I; :?

IH@EA?; ?@ TAF:AM IBB K@;;:LB> >S><E?:@A ;>gE>A<>;

?DI? ;I?:;GC I <@==><?A>;;=>gE:=>H>A?@G I F>;:MAN cA

hijkl mnop mql lrssnotuv wx tju yz{ |}{ ~ronsuq

?D:;<@A?>S?VU>K=@K@;>IG@=HIBIAIBC;:;G=IH>U@=_V

IBB@U:AM F>;:MA>=;?@ F>IB U:?D GIEB? ?@B>=IA<> I??D>

GEA<?:@AIBB>P>B@G?D>F>;:MA>S><E?ILB>;K><:T<I?:@AN

WD>HI:A:A?>=>;? @GU@=_:AM U:?D>S><E?ILB>;K><:TJ

<I?:@A; :;?DI?G@=HIB?><DA:gE>;I=>HE<D H@=>>eJ

<:>A?I??D:;B>P>BVI;;K><:T<I?:@A;I=>E;EIBBC;:HKB>

IAF A@AJF>?>=H:A:;?:<N

> K=@K@;> ?@ E;> I KI=?:<EBI= Ž‘’“”“ ‘•–”’•——“’

˜–”™“ ?><DA:gE> š ›œ ?@ M>A>=I?> IE?@HI?:<IBBCV :G

:? >S:;?;V I L>DIP:@= :HKB>H>A?:AM ?D> E;>=J;K><:T>F

GIEB?J?@B>=IA?K@B:<CV IAF ?@ <@HK@;> :? U:?D ?D> F>J

;:MA;>S><E?ILB>;K><:T<I?:@AV:A@=F>=?@C:>BFI A>U

žŸ —”¡”•—“’Ÿ–” 

¢

“‘£‘Ÿ”•–N cG ;E<D I L>DIP:@= F@>;

A@? >S:;?V ?D:; H>IA; ?DI?V I? :?; <E==>A? F>;<=:KJ

?:@A B>P>BV ?D> F>;:MA :; A@? GIEB?J?@B>=IA?¤ ?D>=> :;

A@ H>IA;?@ K=>P>A?GI:BE=>K=@KIMI?:@A;@= :A<@A;:;J

?>A? >S><E?:@A;N WD> >S><E?ILB> ;K><:T<I?:@A ;D@EBF

D>A<>L> =>F>;:MA>FN

><BI:H ?DI?H@;?GIEB?J?@B>=IA?L>DIP:@=;<IAL>

:A?>=K=>?>F :A ?>=H; @G ”•”Ÿ— •’

¢

Ÿ’”Ÿ— “’¥‘“ ‘•–”¡

– ”˜V I<<@=F:AM ?@ ?D> :A:?:IB G@=HIB ;K><:T<I?:@A @G

?D> F>;:MAN cF>IBBCV U> U@EBF B:_> ?@ G@=HIBBC ;?I?>

¦

™

Ÿ”

”™“ –•§–

Ÿ—

“’¥‘“

•ž Ÿ

Ž“ ¨– V IAF =>gE:=>

?DI? ?D:; A@H:AIB ;>=P:<> L> HI:A?I:A>F G@= IAC >SJ

K><?>F GIEB?@<<E==>A<>N 9:;<=>?><@A?=@BB>=;CA?D>;:;

;D@EBF ?D>A >A;E=> ?D> <@A?:AE:?C @G?D:;;>=P:<>N

WD>=>;EB?:AM GIEB?J?@B>=IA?;K><:T<I?:@A MI?D>=; I

;>? @G K@;;:LB> GIEB? ?@B>=IA? L>DIP:@=;N WD> <D@:<>

L>?U>>A ?D>;> L>DIP:@=; :; @G?>A A@AJF>?>=H:A:;?:<N

cA@=F>=?@F>=:P>IF>?>=H:A:;?:<GIEB?J?@B>=IA?:HKB>J

H>A?I?:@AV I F>TA:?:P> <D@:<> HE;? L> HIF> IH@AM

?D> >S:;?:AM L>DIP:@=;N ©@=>@P>=V ?D> :HKB>H>A?>F

L>DIP:@=HE;?<@HKBC?@?D>I=<D:?><?E=IB<@A;?=I:A?;

@G ?D> :HKB>H>A?I?:@AN cA K=I<?:<>V F:;?=:LE?>F <@AJ

?=@B ;@BE?:@A; I=> @G?>A =>gE:=>FV L><IE;> ?D> ?I=M>?

I=<D:?><?E=>:; F:;?=:LE?>FN cA @=F>= ?@ DIAFB>F:;?=:J

LE?:@AVU><D@;> ?@ IFF=>;;?D> :HKB>H>A?I?:@A ;?>K

§Ÿ– Ÿ——˜N cAF>>FV?D> IE?@HI?:<M>A>=I?:@A @G ‘•§¡

§ –‘Ÿ”–¨ F:;?=:LE?>F <@A?=@BB>=; :; ?D> @ABC K=I<J

?:<IB IB?>=AI?:P> ?@ ?D> HIAEIB F:;?=:LE?:@AV IAF U>

;D@U ?DI? :? U@EBF A@? L> I M@@F <D@:<> M:P>A @E=

GIEB?J?@B>=IA<>M@IBVUD:<DK=@D:L:?;?D>:A?=@FE<?:@A

(3)

clients arbiter

kutŠ

kut‰

kut†

kut ˆ

O:ME=> ¤ b=<D:?><?E=>@G?D> F:;?=:LE?>F I=L:?>=

@G IFF:?:@AIB <@HHEA:<I?:@AN

RA<> IA :HKB>H>A?I?:@A DI; L>>A HIAEIBBC @LJ

?I:A>FV :?; GIEB?J?@B>=IA<> K=@K>=?:>; <IA L> I;;>;;>F

LC <@HKI=:AM :? G@=HIBBC U:?D =>;K><? ?@ ?D> GIEB?J

?@B>=IA? ;K><:T<I?:@A :? UI; F>=:P>F G=@HN > K=@J

K@;> ?@ E;> ?D>

’“£

–“§“–” ‘™“‘–¨ ?><DA:gE> šœ :A

@=F>=?@ I<D:>P>?D:; BI;? ;?>KN

cA ?D> ;>gE>BV U> K=>;>A? @E= M>A>=IB F>;:MA IKJ

K=@I<D IAF :BBE;?=I?> :?; F:>=>A? ;?>K; @A I =EAJ

A:AM >SIHKB>¤ ?D>GEA<?:@AIB ;K><:T<I?:@A @GI GIEB?J

?@B>=IA?F:;?=:LE?>F I=L:?>=N WD>AVU> F:;<E;;?D>=>J

;EB?;@G @E=H>?D@F I;U>BB I;?D>HIAEIB :HKB>H>AJ

?I?:@A I;K><?;VIAFU><@A<BEF>@A ?D>IFPIA?IM>;@G

@E= IKK=@I<DN

8^875^[

Z

[ 5

\^4

56^3]5\ 763^5

6

WD> I=L:?>= H@F>B U> E;> I; I =EAA:AM >SIHKB> :;

:A;K:=>F G=@H šœN c? F>IB; U:?D G@E= <B:>A?; `O:MJ

E=> a U:;D:AM ?@ I<<>;; ;@H> ;DI=>F =>;@E=<>N I<D

<B:>A? ` a <IA =>gE>;? I<<>;; LC I;;>=?:AM

?D> :AKE? ;:MAIB !N WD>I=L:?>==>KB:>; I<<@=F:AMBC

LC I;;>=?:AM ?D> K=@K>= I<_A@UB>FMH>A? ;:MAIB "#$!

IAF K@;;:LBC F>JI;;>=?:AM @?D>= I<_A@UB>FM> ;:MAIB;

"#$%&' (N WD> I=L:?>= HE;?I<D:>P>?U@ LI;:<GEA<J

?:@AIB:?:>;V HE?EIB >S<BE;:@A IAF B:P>A>;;V G@=HIBBC

>SK=>;;>F U:?D ?D><BI;;:<IB ?>HK@=IB B@M:< )W* š œ¤

+ ,-.-/0 1230-4567 8,19

¤ I? IAC H@H>A?V I?

H@;? @A>I<_A@UB>FM>;:MAIB <IA L>I;;>=?>F¤

:; ¤ <=`>?@`"#$A"#$B C "#$A"#$D C

"#$A"#$E C"#$B"#$D C"#$B"#$E C"#$D"#$Eaa

+ F5GH7H44 8 FIJ9

¤G@=>I<D <B:>A?V:GI =>gE>;?:;

I;;>=?>FV?D>A :? :; >P>A?EIBBC I<_A@UB>FM>F¤

WD> I=L:?>= F@>; A@? H>H@=:P> :A<@H:AM =>gE>;?;N

WDE;V ?@ ;I?:;GC KLM!V U> HE;? I;;EH> ?DI? >I<D

<B:>A? :; K>=;:;?>A?¤ :? HI:A?I:A; ! I? B>I;? EA?:B

=><>:P:AM "#$!N d@U>P>=V :G ! :; F>I;;>=?>F L>G@=>

@L?I:A:AM "#$!V?D>A :? ;DIBB A@? L> I<_A@UB>FM>F I?

IBBN cA @=F>= ?@ :HKB>H>A? B:P>A>;;V I ?@_>A H><DIJ

A:;H :; E;>FN I<D <>BB :; K>=:@F:<IBBC M:P>A K=:@=:?C

U:?D =>;K><? ?@ ?D> @?D>=;N I<D ?@_>A :; PIB:F G@=

@ABC @A> ;:AMB>?:H> EA:? `>S><E?:@A <C<B>a IAF ?D>A

>SK:=>; >P>A ?D@EMD :? DI; A@? L>>A <@A;EH>FN b?

IAC ?:H>V I? H@;? @A> ?@_>A HIC <:=<EBI?> ?D=@EMD

?D> <>BB;N WD> ?@_>A :; ?=IA;H:??>F P:I ?D> K@:A?J

?@JK@:A? F>F:<I?>F <@HHEA:<I?:@A B:A_; Q! ` a

>;?ILB:;D>F L>?U>>A <@A;><E?:P><>BB;N WD><>BB HIC

@ABC I<_A@UB>FM> :?; <B:>A? :G :? :; D@BF:AM ?D> ?@_>A

I??D><E==>A?<C<B>N d@U>P>=V:A <I;>#QQ! :;A@? <E=J

=>A?BC D@BF:AM ?D> ?@_>AV ?D>A :? HIC ;?:BB I<_A@UBJ

>FM>:?;<B:>A?I<<@=F:AM?@IU>I_K=:@=:?CK@B:<C¤ ?D>

<>BB;I=>@=F>=>FI<<@=F:AM?@I;?I?:<K=:@=:?C;<D>H>V

G=@H #QQAV UD:<D DI;?D> D:MD>;? K=:@=:?C ?@ #QQEN cG

?D><>BB <E==>A?BCD@BF:AM ?D>?@_>A F@>;A@? DIP> IA

:A<@H:AM =>gE>;?V ?D>A @?D>= <>BB; HE;? L> ILB> ?@

I<_A@UB>FM> ?D>:= :A<@H:AM =>gE>;?;V K=@P:F>F HEJ

?EIB >S<BE;:@A :; =>;K><?>FN WDE;V :G #QQ! =><>:P>; IA

:A<@H:AM =>gE>;? UD:B> A@? D@BF:AM ?D> ?@_>AV ?D>A

:? HIC I<_A@UB>FM>?D:; =>gE>;? @ABC :G ?D>=> I=>A@

H@=> K=:@=:?I=C =>gE>;?; `<>BB; ' R a IAF :G

A@A> IH@AM ?D> B>;; K=:@=:?I=C <>BB; ` $ C a:;

IL@E??@ I<_A@UB>FM>:?;<@==>;K@AF:AM=>gE>;?UD:B>

D@BF:AM ?D> ?@_>AN

O:AIBBCV U> U:;D @E= I=L:?>= ?@ DIP> I F:;?=:LE?>F

I=<D:?><?E=>¤ G@E= <>BB;V >I<D <@==>;K@AF:AM ?@ @A>

<B:>A?N

S TU

6U^

V

[ []6 W

5[\

XYZ [\]^_`a bccdc`a \ef g\h^]cb`

WD:; :;?D>GEAFIH>A?IB <IE;IB K=:A<:KB>:A ?D>;?EFC

@G GIEB? KI?D@B@MC IAF ?D> F>;:MA @G F>K>AFILB> ;C;J

?>H; šœN b GIEB? HICC:>BF IA >==@=¤ I KDC;:<IB DIPJ

I=F@E; >P>A? HIC C:>BF I B@M:<IB :A?>=AIB :A<@A;:;J

?>A<C @G ?D> ;C;?>HN bA >==@= HIC C:>BF I GI:BE=> @G

@A>@=H@=><@HK@A>A?;N b GI:BE=>@G@A><@HK@A>A?

<IA L> P:>U>F I; I GIEB? I? ?D> ;C;?>H B>P>BN I<D

K@;;:LB>GI:BE=>:; K>=HIA>A?N

cA @E= <@A?>S?V U> ?=>I? K=:HI=C GIEB?; ?DI? <IA

@ABC L> KDC;:<IB >S?>=AIB >P>A?;N > B:H:?@E= ;?EFC

?@ “’’•’

¢

’•‘“–¨¤ U>I;;EH>?D>=>>S:;?;I =>B:ILB>

>S?>=AIB EA:?V UD:<D =>K@=?; IA >==@= :G IAF @ABC :G

I KDC;:<IB GIEB? DI; @<<E==>FN OI:BE=> HIAIM>H>A?

HIC :AP@BP>L@?D DI=FUI=>IAF;@G?UI=>@=?>HK@=IB

=>FEAFIA<CN cA@E=<@A?>S?VU>=>BC@A?D>HIAEIB:AJ

?=@FE<?:@A @G DI=FUI=> =>FEAFIA<CV G@BB@U>F LC ?D>

IE?@HI?:< M>A>=I?:@A @G =>FEAFIA? ;@G?UI=>V UD:<D

>SKB@:?; L@?D ?D> >S:;?:AM IAF ?D> =>FEAFIA? DI=FJ

UI=>N

WD> F>;:MA @G F>K>AFILB> ;C;?>H; <IBB; G@= I F>FJ

(4)

DCK@?D>;:;V?D> GI:BE=>H@F>B IAF ?D>GIEB? ?@B>=IA<>

K@B:<CN cA ?D:; ;><?:@AV U> @E?B:A> ?D>;> ?D=>> K@:A?;

G=@H I M>A>=IB K@:A? @G P:>UV L>G@=> ;K><:GC:AM ?D>H

G@=HIBBCU:?D=>;K><??@@E=KI=?:<EBI=K=@LB>H :A?D>

A>S? ;><?:@AN

XY behe \

b GI:BE=> DCK@?D>;:; ;?I?>; UD:<D <@HK@A>A?; @G ?D>

;C;?>H HICGI:BN cGH@=>?DIA@A><@HK@A>A?:;B:_>BC

?@GI:BVžŸ— ’“‘•–£¨ ’Ÿ”•–I=>I<@HH@AUIC?@>SJ

K=>;; ;EL;>?; @G <@HK@A>A?; ?DI? HIC GI:B ?@M>?D>=N

b<<@=F:AM ?@ ?D:; DCK@?D>;:;V ?D> =>HI:A:AM <@HK@J

A>A?; I=> ;EKK@;>F ?@ L> =>B:ILB>¤ ?D>C A>P>= GI:BV

@= :G ;E<D I GI:BE=> @<<E=;V ?D> UD@B> ;C;?>H GI:B;N

WD> GI:BE=> DCK@?D>;:; A>>F; ?@ L> <@AT=H>F LC I

;?@<DI;?:<IAIBC;:;;?>KV:A @=F>=?@ TAF?D>K=@LIL:BJ

:?C G@= >I<D GI:BE=> <@ATME=I?:@AN cA ?D:; F@<EH>A?V

U>I;;EH>?DI?IBBGI:BE=><@ATME=I?:@A;;K><:T>FI=>

>gEIBBC K=@LILB>N

XYX behe \

D>AI<@HK@A>A?GI:B;V;K><:GCUDI??D:;GI:BE=>:HJ

KB:>;N WD:; IH@EA?; ?@ F>TA:AM I L>DIP:@= ?DI? :;

?=:MM>=>FLC?D:;GI:BE=>IAF ?DI? H:MD?:AE>A<>?D>

L>DIP:@=@G?D>=>HI:A:AM <@HK@A>A?;N O @= :A;?IA<>V

UD>A I <@HK@A>A? GI:B; `K=@<>;;@=V <@HHEA:<I?:@A

B:A_V;>A;@=V>?<NaV:? HIC;?@K =>I<?:AM?@ :?;>AP:=@AJ

H>A?N WD:;H>IA;>:?D>= ;>AF:AM I <@A;?IA?PIBE>V@=

;>AF:AM =IAF@H PIBE>; ?@ ?D> >AP:=@AH>A? ` CPIAJ

?:A> L>DIP:@=aV @= ;>AF:AM A@ PIBE> I? IBB `GI:BJ;IG>

L>DIP:@=aN

XY behe \

cF>IBBCV I GIEB?J?@B>=IA? ;C;?>H ;D@EBF HI:A?I:A :?;

GEA<?:@AIB:?:>; IAF :?;K>=G@=HIA<> `A@H:AIB ;>=P:<>a

>P>A ?D@EMD ;@H> @G :?; <@HK@A>A?; I=> F@UAN cA

K=I<?:<>V?D:; I;;EHK?:@A :; ?@@ ;?=:<? IAF >SK>A;:P>

?@:HKB>H>A?N WDE;V:A<I;>IGI:BE=>@<<E=;V?D>A@HJ

:AIB ;>=P:<>HIC L> =>KBI<>F LC I Ž“¨’ŸŽ“Ž •

¢

“’Ÿ”–¨

§•Ž“N D>A?D>;C;?>H=EA;:A;:F>IF>M=IF>FH@F>V

@ABCI ;EL;>?@G:?;:A:?:IBGEA<?:@AIB=>gE:=>H>A?;I=>

;?:BB H>?N > U:;D ?@ I<D:>P>GIEB?J?@B>=IA<> LC ;>?J

?B:AM ;E<D I F>M=IF>F @K>=I?:AM H@F> UD>A I GI:BE=>

@<<E=;N cA@E=<@A?>S?V?D:; :; F@A>LC >SK=>;;:AM ?D>

IKK=@K=:I?> <@A;?=I:A?; ?DI? I=> E;>F ?@ <@A?=@B ?D>

;C;?>H;L>DIP:@=G=@H @E?;:F>V:A @=F>= ?@ IP@:FEAJ

UIA?>F <@ATME=I?:@A;?DI? HICL><@H> =>I<DILB>:A

<I;> @G I GI:BE=>N WD:; IKK=@I<D @ABC IKKB:>; ?@ ;C;J

?>H; ?DI? I=> ‘•–”’•——Ÿ—“¤ G@= ;E<D ;C;?>H;VI ;>? @G

F>F:<I?>F ‘•–”’•——Ÿ—“ –

¢

 ” :; K=@P:F>F G@= ;>=P:<>

HI:A?>AIA<> KE=K@;>;N WD> ;C;?>H L>DIP:@= :; <@AJ

;?=I:A>F LC F=:P:AM ?D> <@A?=@BBILB>:AKE?; IKK=@K=:J

I?>BCN bBB=>HI:A:AM:AKE?PI=:ILB>;I=><IBB>F  –‘•–¡

”’•——Ÿ—“N WD> F:;<=>?> <@A?=@BB>= ;CA?D>;:; ?><DA:gE>

š ›œ :; IA >S<>BB>A? <D@:<>G@= IE?@HI?:<IBBC K=@FE<:AM

IH@EA?; ?@ IFF:AM ;EKKB>H>A?I=C DI=FUI=> `:AKE?

PI=:ILB>; IAF IFF:?:@AIB ;?I?>; IAF ?=IA;:?:@A;a G@=

LI<_EK KE=K@;>;N WD:; :; ;CA@ACH @G ;K><:GC:AM

I DI=FUI=> =>FEAFIA<C H><DIA:;HN RA ?D> @?D>=

DIAFV ?D> =>;EB?:AM ;CA?D>;:P>F <@A?=@BB>=V :G :? >SJ

:;?;V =>K=>;>A?; I K=@M=IH `;@G?UI=> =>FEAFIA<Ca

?DI? IKK=@K=:I?>BC E;>; ?D>

Ÿ—’“ŸŽ

˜ “ ”–¨ =>FEAJ

FIA?DI=FUI=>:A @=F>=?@ >;?ILB:;D ?D>F>M=IF>F @KJ

>=I?:AM H@F>N

9:;<=>?><@A?=@BB>=;CA?D>;:;A>>F;I G@=HIB ‘•–”’•—

•

“‘”¥“N cA @E= G=IH>U@=_V ?D:; <@A?=@B @L><?:P>

HE;?>SK=>;;GIEB??@B>=IA<>N WD:;<IA L>I<D:>P>F:A

?U@ UIC;¤

N fK><:GC D@U I GI:BE=> ;D@EBF L> DIAFB>FN WD:;

<IA L> F@A> UD>A>P>= ?D> LI<_JEK K=@<>FE=>

:; _A@UA IJK=:@=:V @= UD>A ?D:; K=@<>FE=> HE;?

<@HKBC?@ I K=>JF>TA>F ;?IAFI=FN WD>=>;EB?:AM

<@A?=@BB>=;D@EBFF=:P>?D><@A?=@BBILB>:AKE?;I<J

<@=F:AMBCN

N fK><:GC UDI? ?D> ;C;?>H ;D@EBF IBUIC; F@V F>J

;K:?> GI:BE=> @<<E==>A<>;N b F>M=IF>F ;>=P:<>

:; G@=HIBBC ;K><:T>F IAF ?D> =>;EB?:AM <@A?=@BB>=

HE;? <@A;?=I:A ?D> ;C;?>H ;@ ?DI? ?D:; ;>=P:<>:;

I<D:>P>FN

[6W7 ! 4

8^!^Z

"

5

76

3^5

6 \

Z

\73^ ^5!

YZ [\h^]cb #$%d_#b`h`

> I;;EH>?DI? @ABC ?D> <@HHEA:<I?:@A B:A_; Q! L>J

?U>>A<>BB;HICGI:BN D>AB:A_Q! GI:B;V:?;?@K;?=IA;J

H:??:AM?@_>A;?@?D><>BBN I<DB:A_:;GI:BJ;:B>A?IAF

:?; GI:BE=> :; K>=HIA>A?N WDE;V K@?>A?:IBBCV?D> <>BB

HIC A>P>= L> I<_A@UB>FM>F IACH@=>N ©@=>@P>=VU>

;DIBB I;;EH> ?DI? ?D> K=@LIL:B:?C ?@ DIP> I GI:BE=>

I><?:AM H@=>?DIA @A> B:A_ :; A>MB:M:LB>N

Y &he' g\h^]cb (dfb^

bA IL;?=I<? H@F>B G@= >I<D <@HHEA:<I?:@A B:A_ :;

M:P>AO:ME=>N I<DB:A_HICL>>:?D>=GEA<?:@AIBV:A

UD:<D <I;>:? ?=IA;H:?; <@==><?BC?D> ?@_>A; IAF K=:J

@=:?C HIAIM>H>A? :AG@=HI?:@AV @= :A I GI:BE=> ;?I?>V

:AUD:<D<I;>:?;?@K;?=IA;H:??:AM G@=>P>=N WD>?=IAJ

;:?:@A ?@ ?D> GI:BE=> ;?I?>:;?=:MM>=>FLC ?D>>AP:=@AJ

H>A? IAF <@==>;K@AF; ?@ I KDC;:<IB FIHIM>>P>A?N

WD> ;?I?:< K=:@=:?C L>?U>>A ?D> <>BB; :; F>TA>F E;J

:AM IA @P>==:F>QM=IA? H><DIA:;HN WDE;V <>BB @P>=J

=:F>;<>BB C: ! :;I<?:P>@=:G <>BBR@P>==:F>;

<>BB N WD> T=;? <>BB :A ?D> <DI:A ` <>BB a <IAA@? L>

@P>==:FF>AN RA?D> @?D>=DIAFV<>BB M=IA?;<>BB R

: :?:;M=IA?>F :?;>BGLC<>BBCIAF:G:? :;A@?D@BFJ

:AM L@?D IA :A<@H:AM =>gE>;? IAF I ?@_>AN WD> BI;?

<>BB :A ?D> <DI:A `<>BB a :; IBUIC; M=IA?>FN

I<D <>BB :; IUI=> @G ?D> ;?I?> `=EAA:AM @= GI:BJ

(5)

running

failure

!

!

!

O:ME=> ¤ bL;?=I<?H@F>B @G I <@HHEA:<I?:@A B:A_ Q!

D>A B:A_ Q! :; F@UAV <>BB ;?@K; =><>:P:AM ?@_>A;N

WDE;V:?;?@K;<@HKBC:AM U:?D?D>;K><:T<I?:@AKLM!N

©@=>@P>=V I B:A_ GI:BE=> :APIB:FI?>; ?D> ;?I?:< K=:@=J

:?C ;<D>H>VI; A@ <>BB <IA L>IUI=> IACH@=>@G @?D>=

=>gE>;?;@GD:MD>=QB@U>=K=:@=:?CN

YX [\]^_ _d^bc\eb %d^h$

D>A B:A_ Q! :; F@UAV ?D> ?@_>A _>>K; H@P:AM EA?:B

:? =>I<D>; Q!V IAF ?D>A :? :; B@;?N O=@H ?DI? H@H>A?V

A@ @?D>= =>gE>;? U:BB >P>= L> I<_A@UB>FM>FN WDE;V

?D>HE?EIB >S<BE;:@A=>gE:=>H>A?:;;?:BB?=:P:IBBC;I?J

:;T>FVLE? ?D> =>;K@A;> ?:H> :; A@ B@AM>= MEI=IA?>>F

G@= IAC <>BBN bB;@V ?D> ;?I?:< K=:@=:?C ;<D>H> :; F:;J

ILB>FN

WD> GIEB?J?@B>=IA<> K@B:<C HE;? IFF=>;; ?D> =>J

;K@A;>?:H>K=@LB>HVUD:B> ;?:BB >A;E=:AM HE?EIB >SJ

<BE;:@AN b; U> _A@U ?DI? :A :?; F>M=IF>F H@F>V@E=

I=L:?>= F@>; A@? <@HKBC U:?D ?D> =>;K@A;> ?:H> =>J

gE:=>H>A?VU>U:;D?@ IKK=@K=:I?>BC<@A;?=I:A:?;L>J

DIP:@=V;@?DI??D>=>;K@A;>?:H>L><@H>;I<<>K?ILB>N

> ;DIBBE;>?D> <@A?=@BB>= ;CA?D>;:;?><DA:gE>:A @=J

F>= ?@ K=@FE<> IKK=@K=:I?> <@A?=@BB:AM <@A;?=I:A?;N

d@U>P>=V:A :?; <E==>A? F>;:MA ;?I?>V @E= I=L:?>= DI;

P>=C G>U K@;;:LB> L>DIP:@=; IAF <IA DI=FBC L> <@AJ

?=@BB>F¤ :? ;D@EBF L> IP@:F>F ?@ <@A;?=I:A ?D> :A<@HJ

:AM =>gE>;? @= >==@= ;:MAIB;V I; =>gE>;?; IAF >==@=

>P>A?; ;D@EBF L> ILB> ?@ I==:P> I? IAC H@H>A?N >J

;:F>;V ?D> @ABC UIC ?@ <@A;?=I:A ?D> L>DIP:@= @G I

=>I<?:P> ;C;?>H :; P:I :?; :AKE? ;:MAIB;N WDE;V :A @=J

F>=?@ I<D:>P>?D:;GIEB?J?@B>=IA<>K@B:<CVU>HE;?=>J

F>;:MA @E= I=L:?>= :A?>=GI<>IAF L>DIP:@=V?@ HI_> :?

H@=> <@A?=@BBILB>N

57 367.600/505.

D>A IB:A_:;F@UAV?D>

I=L:?>= ;?@K; <@HKBC:AM ?@ :?; ;K><:T<I?:@A I; ;@@A

I; ?D> ?@_>A :; B@;?N WDE;V I K@;;:LB> ;EKKB>H>AJ

?I=C <@A?=@B ;@BE?:@A :AP@BP>; IFF:AM I Ÿ‘ 

¢

”•“–

:A;>=?:@A K@:A? H><DIA:;H ` O:ME=> aN WD> I=L:?>=

>AP:=@AH>A? <IA =>:A;>=? I A>U ?@_>A LC IF>gEI?>BC

<@A?=@BB:AM ?D:; ;EKKB>H>A?I=C :AKE?N d@U>P>=V :G Q!

!"##$

%"&$

'!($

'!(*+ ,-(".$

O:ME=> ¤ )>BB :A?>=GI<>U:?D DI=FUI=> =>FEAFIA<C

> =>F>;:MA ?D> I=L:?>= LC I;;EH:AM ?D> >S:;J

?>A<> @G IA >S?>=AIB MB@LIB  

¢

“’¥•’N C I;;>=?J

:AM ?D> /"#$01 @?$>! ;:MAIBV ?D:; ;EK>=P:;@= :A;>=?;

I A>U ?@_>A :A;:F> ?D> I=L:?>=N C F>I;;>=?:AM ?D>

/"#$01 @?$>! ;:MAIBV :? K=>P>A?; I A>U ?@_>A G=@H

L>:AM :A;>=?>FN O:=;?V LI<_EK ?@_>A; ;D@EBF @ABC L>

:A;>=?>FUD>AI?B>I;?@A>B:A_:;F@UAN f><@AFVUD>A

?D:; :;?D> <I;>V?@_>A; ;D@EBF A@?L>:A;>=?>F?@@ @GJ

?>AV I; I? H@;? @A> ?@_>A ;D@EBF <:=<EBI?> :A;:F>?D>

I=L:?>=N O:AIBBCV ?@_>A :A;>=?:@A ;D@EBF L> F@A> K>J

=:@F:<IBBCV ;@ ?DI? >I<D :A<@H:AM =>gE>;? :; I<_A@UBJ

>FM>F U:?D I =>I;@AILB>=>;K@A;>?:H>N

Y 2#hb3he ^h3beb`` de_cd^ d45b6

_h3b`

7K ?@ A@UV F:;<=>?> <@A?=@BB>= ;CA?D>;:; DIAFB>;

;IG>?C IAF A@AJLB@<_:AM @L><?:P>;N cA @=F>= ?@ IFJ

F=>;;?D>B:P>A>;;>AG@=<>H>A?K=@LB>HVU>DIP><D@J

;>A ?@ =>KBI<>?D><@A<>K?@G =>;K@A;>:ATA:?>?:H>

LC I • –Ž“Ž ”§“ =>;K@A;> =>gE:=>H>A?V UD:<D :;

H@=>>I;:BC ;@BPILB> LC <E==>A?BC IPI:BILB> <@A?=@BB>=

;CA?D>;:;IBM@=:?DH;N WD:; =>gE:=>; TAF:AM I =>I;@AJ

ILB> L@EAF @A ?D> =>;K@A;> ?:H> G@= >I<D "#$! ;:MJ

AIBN f:A<>?D>=>I=>G@E=<>BB;VIAF;:A<>I? >I<D<C<B>

I A>U <>BB =><>:P>; ?D> ?@_>AV U> ;>? ?D> =>;K@A;>

L@EAF ?@ G@E= <C<B>;N WDE;V?D> B:P>A>;;=>gE:=>H>A?

IFIK?>F ?@ L@EAF>F ?:H>L><@H>;¤

KLM8

!

¤ <=` ! N "#$! C <9` "#$! C<9` "#$! C

<9`"#$!C<9` "#$!aaaaa

C <@HL:A:AM ?D> @L><?:P>; :; IAF KLM8

!

`

aVU>@L?I:A I <@A?=@BB>=DIP:AM ?D>G@BB@U:AM G>IJ

?E=>;¤

+

:? @L;>=P>; >P>=CPI=:ILB>:A ?D> ;C;?>H:

+

:? :; @ABC IBB@U>F ?@ <@A?=@B ?D> :AKE?;

/"#$01 @?$>! ` a :A @=F>= ?@ <@A;?=I:A

?D>I=L:?>=?@ I<D:>P>:?;GEA<?:@AIB=>gE:=>H>A?:

+

I<<@=F:AM?@?D><@A?=@B@L><?:P>;V:GB:A_Q! GI:B;V

?D> <@A?=@BB>= U:BB =>>;?ILB:;D ?D> MB@LIB ;C;?>H

<@D>=>A<>LC K@;;:LBC =>:A;>=?:AM LI<_EK ?@_>A;

?D=@EMD <>BB V UD:B> K=>P>A?:AM ;E<D ?@_>A :AJ

;>=?:@A;UD>A>P>=?D:; U@EBFP:@BI?>?D> :; =>J

gE:=>H>A?N

(6)

Z

7Z5 3

7U^[6

> DIP>H@F>B>F @E= I=L:?>= IAF U> DIP> PIB:FI?>F

:?;GIEB?J?@B>=IA<><IKIL:B:?CVLCI<?EIBBC;CA?D>;:P:AM

I <@A?=@BB>=UD:<D >A;E=>;IBB?D>=>gE:=>H>A?;;?I?>F

:Af><?:@AN O@=>SIHKB>V:GB:A_QAGI:B;V?D>G@BB@U:AM

;<>AI=:@; I=> K@;;:LB>¤

+

A :; I;;>=?>F IAF B& DV IAF E I=> IBB

F>I;;>=?>FN A :; I<_A@UB>FM>FN

+

A :; I;;>=?>FN cG B& DV IAF E I=> I;J

;>=?>F IAF :G B:A_; QB&QDV IAF QE I=> @K>=I?:@AIBV

?D>A ?D><@A?=@BB>=>AG@=<>;?D>GI:= I<_A@UB>FMJ

H>A? @G IBB ?D> =>gE>;?;V LC :A;>=?:AM I LI<_EK

?@_>A ?D=@EMD <>BB N WD> ?@_>A :A;>=?:@A ?I_>;

:A?@ I<<@EA? ?D> =>;K@A;> F>BIC L@EAF @G >I<D

<>BBN WDE;VI K@;;:LB> GE?E=> P:@BI?:@A @G ?D> F>J

BIC =>;K@A;> L@EAF :; Ÿ–”‘

¢

Ÿ”“Ž IAF IP@:F>FV

LC >AG@=<:AM ?D> :A;>=?:@A @G I ?@_>A I? ?D> IKJ

K=@K=:I?>H@H>A?N

+

cG <>BB ' `' a D@BF; I ?@_>AV ?D>A ?D> <@AJ

?=@BB>= F:;ILB>;?D>:A;>=?:@A@GIA>U LI<_EK?@J

_>A EA?:B ?D> <E==>A?BC >S:;?:AM ?@_>A :; B@;? :AJ

;:F>?D> GI:B>F B:A_ Q!N

WD> <@A?=@BB>F I=L:?>= @L?I:A>F :; –•–¡Ž“”“’§–”‘N

WD> <@A?=@B UD:<D DI; L>>A ;CA?D>;:P>F :; <IBB>F

§

Ÿ

§

Ÿ—

—˜

¢

“’§¥“¤ <@A?=@BBILB> :AKE?; I=> @ABC

<@A;?=I:A>F :A <I;> @G A><>;;:?C U:?D =>;K><? ?@ ?D>

<@A?=@B @L><?:P>;N cAF>>FV :G B:A_ Q! :; @K>=I?:@AIBV

?D> PIBE> @G ?D> <@A?=@BBILB> :AKE? /"#$01 @?$>!

F@>; A@? :AE>A<> ?D> L>DIP:@= @G?D> I=L:?>=VI; U>

<D@;> LC <@A;?=E<?:@AN cG B:A_ Q! :; F@UAV ?D> :AKE?

/"#$01 @?$>! @ABC A>>F; ?@ L> <@A;?=I:A>F :A ?U@

;K><:T< ;<>AI=:@;¤

+

b; B@AM I; ?D> ?@_>A =:AM <@A?I:A; I ?@_>AV

/"#$01 @?$>! :; ;>? ?@ "QN

+

D>A ?D>?@_>A =:AM L><@H>; >HK?C `?D> ?@_>A

M>?; B@;? LC B:A_ Q!aV ?D> <@A?=@BB>= >AG@=<>; ?D>

:A?=@FE<?:@A@GI A>U LI<_EK?@_>A @ABC UD>AI

K@;;:L:B:?C >S:;?; ?DI? I =>gE>;? :; A@? I<_A@UBJ

>FM>F U:?D:A ?D> J<C<B> ?:H> L@EAFN cG @ABC

@A> :A<@H:AM =>gE>;? :; I<?:P> I? I ?:H>V :? :;

:HH>F:I?>BC I<_A@UB>FM>FVU:?D@E? I A>>F G@=I

?@_>AN f?:BBV :A ;E<D I ;:?EI?:@AVI ?@_>A HIC L>

:A;>=?>FN

WD> =>;EB?:AM <@A?=@BB>F I=L:?>= I<?EIBBC @>=; I

<D@:<> IH@AM ;>P>=IB IPI:BILB> GIEB?J?@B>=IA? L>DIPJ

:@=;N ><IE;>@G:?;A@AJF>?>=H:A:;?:<AI?E=>VU><@AJ

;:F>=?D:;=>;EB?I;I A>UBCM>A>=I?>F “ “‘ ”Ÿ—“

¢

“‘¡

£‘Ÿ”•– UD:<D >HL>F; I ;>? @G GIEB?J?@B>=IA? L>DIPJ

Y " Z U "

5

7] 55[ 67Z5 763^5

6

b? ?D:; ;?IM>V@L?I:A:AM I K@;;:LB>:HKB>H>A?I?:@A @G

?D>GIEB?J?@B>=IA? I=L:?>= U@EBF :AP@BP><D@@;:AM •–“

:A?>=>;?:AM L>DIP:@=IH@AM ?D@;>IBB@U>FLC?D>>S>J

<E?ILB> ;K><:T<I?:@A IAF >SK=>;;>F :A ?D> <@A?=@BB>F

I=L:?>=VU:?D ?D>IFF:?:@AIB <@A;?=I:A??DI? ?D>=>;EB?

HE;? L> Ž“”“’§–”‘N

WD> I=<D:?><?E=> @G ?D> =>;EB?:AM <@A?=@BB>= HE;?

IB;@ <@HKBC?@ ?D>:A:?:IB GI:BE=>DCK@?D>;:;N b<<@=FJ

:AM ?@?D:;DCK@?D>;:;V@ABC<@HHEA:<I?:@AB:A_;HIC

GI:BN WDE;VU>HE;?I;;EH>?DI??D><@A?=@BB>=<IAA@?

GI:BN 7AG@=?EAI?>BCV ?D> =>;EB?:AM <@A?=@BB>= I<D:>P>;

¨—•Ÿ—‘•–”’•— Ÿ–Ž •“’¥Ÿ”•–:?DE;V;E<DIAI;;EHKJ

?:@A :;A@?=>IB:;?:<U:?D=>;K><??@ ?D>F:;?=:LE?>FI=J

<D:?><?E=>@G?D> I=L:?>=N d>A<>V ?D> :HKB>H>A?I?:@A

@G ?D> <@A?=@BB>F I=L:?>= HE;? IB;@ H>>? ?D> I=<D:J

?><?E=IB <@A;?=I:A?¤ “Ÿ‘™ ‘“—— ™• —Ž “ —•‘Ÿ——˜ ‘•–¡

”’•——“ŽV IAF ?D> @ABC PI=:ILB>; ?D> B@<IB <@A?=@BB>= :;

IBB@U>F?@H@A:?@=;D@EBF L>?D>:A?>=AIBPI=:ILB>;@G

<>BB N WD> IE?@HI?:< M>A>=I?:@A @G B@<IB <@A?=@BB>=;

I<D:>P:AM MB@LIB <@A?=@B @L><?:P>; :; I HE<D H@=>

F:e<EB? ?I;_V _A@UA I; Ž“‘“–”’Ÿ—“Ž ‘•–”’•——“’ ˜–¡

”™“ šœN WD> >S:;?>A<> @G I F:;?=:LE?>F <@A?=@B ;@J

BE?:@A @G?>A =>gE:=>; ;EKKB>H>A?I=C <@HHEA:<I?:@A

L>?U>>A ?D> B@<IB <@A?=@BB>=;N cA @E=<@A?>S?VI;;EHJ

:AM ’“—Ÿ—“ <@HHEA:<I?:@A L>?U>>A B@<IB <@A?=@BB>=;

U@EBF <@A?=IF:<? @E= :A:?:IBGI:BE=>DCK@?D>;:;VUD:<D

;?I?>; ?DI? <@HHEA:<I?:@A L>?U>>A <>BB; :; A@? =>B:J

ILB>N RA ?D> @?D>= DIAFV ?D> F:;?=:LE?>F <@A?=@BB>=

;CA?D>;:; K=@LB>H U:?D@E? <@HHEA:<I?:@A L>?U>>A

B@<IB<@A?=@BB>=;DI;L>>A;D@UA?@L>EAF><:FILB>šœN

b; I <@A;>gE>A<>V U> LE:BF ?D> B@<IB <@A?=@BB>=;

HIAEIBBCN C <@A;?=E<?:@AV @E= I=L:?>= DI; ;>P>=IB

:A?>=>;?:AM K=@K>=?:>;N O:=;? @G IBBV ?D> <@A?=@BBILB>

:AKE?;I=> F@A?<I=>; I;B@AM I;A@ B:A_GI:BE=>DI;

@<<E==>FN WD>AV I<<@=F:AM ?@ ?D> GI:BE=>DCK@?D>;:;V

@ABC @A> B:A_ HIC GI:BN WDE;V UD>A B:A_ Q! :; F@UAV

@ABC:?;<@==>;K@AF:AM/"#$01 @?$>!A>>F;?@L><@AJ

?=@BB>FN O:AIBBCV LC =EAA:AM I ;Ee<:>A? ;>? @G ;:HEJ

BI?:@A ;<>AI=:@;V U> =>IB:P>?DI? ?D>=> >S:;?; I ;>? @G

?=I<>;?DI?I=>IBB@U>FLC?D><@A?=@BB>FI=L:?>=;K><:J

T<I?:@AIAF?DI?<IAL>KBIC>F@A/"#$01 @?$>!N bBB

?D>;>?=I<>;I=><@HK@;>FLC?D>G@BB@U:AM;E<<>;;:P>

KI=?;¤ `a IA I=L:?=I=C B>AM?D K=>TSV <@==>;K@AF:AM

?@ ?D> A@=HIB @K>=I?:@AV L>G@=> IAC B:A_ GI:BE=> @<J

<E=;:IBB IB@AM?D:;K=>TSV/"#$01 @?$>! <IAL>;>??@

IACPIBE>: ` a@A<>IGI:BE=>@<<E=;VI L@EAF>FJB>AM?D

K=>TS G@BB@U;V <@==>;K@AF:AM ?@ ?D> ?@_>A K=@KIMIJ

?:@A EA?:B :? :; B@;?: ` a TAIBBCV I K>=:@F:< ;EeS <@=J

=>;K@AF:AM?@ ?D>K>=:@F:<=>:A;>=?:@A @GI A>U ?@_>A

:A;:F>?D> I=L:?>= @A<>?D> K=>P:@E;@A> :; B@;?N

fE<D I L>DIP:@= :; —•‘Ÿ— ?@ >I<D <>BB IAF <IA L>

=>K=@FE<>F LC I ;:HKB> HIAEIBBC LE:B? F>?>=H:A:;J

?:< TA:?> ;?I?> HI<D:A>V ;E<D I; ?D> @A> K=>;>A?>F

O:ME=> N d>A<>V LC <@HK@;:AM ?D> I=L:?>= U:?D

G@E= :A;?IA<>; @G ?D:; ;?I?> HI<D:A>V GIEB?J?@B>=IA<>

(7)

arbitrary length prefix

prefix fixed length

periodic suffix

!

!

O:ME=> ¤ @;;:LB> :HKB>H>A?I?:@A @G I B@<IB <@AJ

?=@BB>= G@= <>BB

<E=N

b;;>;;:AM ?D> <@==><?A>;; @G ?D> IL@P> :HKB>H>AJ

?I?:@A :; I ;?=I:MD?G@=UI=F ?I;_ IAF <IA L> F@A> LC

;:HEBI?:@AN d@U>P>=V :A M>A>=IBV ;E<D IA >SDIE;J

?:P> P>=:T<I?:@A ?I;_ <IA L><@H> P>=C F:e<EB? I;

;@@A I; ?D> F>;:MA L><@H>; H@=> <@HKB>SN O @=HIB

P>=:T<I?:@A ?><DA:gE>; I=> _A@UA ?@ F>IB H@=> >eJ

<:>A?BCU:?D?D:; K=@LB>HV>P>A UD>AIKKB:>F @A =>IBJ

B:G> F>;:MA;N cA KI=?:<EBI=V ?D>

’“£

–“§“–” ‘™“‘–¨

?><DA:gE> šV œ :;E;>F G@=I;;>;;:AM:HKB>H>A?I?:@A;

IMI:A;?I A@AJF>?>=H:A:;?:<@K>=I?:@AIB ;K><:T<I?:@AN

WD> E;> @G ?D:; ?><DA:gE> :A @E= <@A?>S? :; >><?:P>

G@= ?U@ HI:A =>I;@A;¤ T=;? @G IBBV :G IA :HKB>H>AJ

?I?:@A ’“£–“ I ;K><:T<I?:@AV ?D>A :? :AD>=:?; >P>=C

R)W* K=@K>=?C ;I?:;T>F LC ?D> ;K><:T<I?:@A šœN

@?>V D@U>P>=V ?DI? ?D:; <@A;>=PI?:P> G>I?E=> @ABC

<@A<>=A; K=@K>=?:>; U=:??>A :A R)W*N cA @E= <@AJ

?>S?V ?D> GIEB?J?@B>=IA<> @L><?:P>; :; IAF KLM!V

` a I=> <@HKB:IA? ?@ ?D> R)W* ;EL;>? @G

)W*Nf><@AFV=>TA>H>A?<D><_:AM:;I HI?E=>K=@<>J

FE=> UD:<D <IA >S?>A;:P>BC =>BC @A <@HK@;:?:@AIB:?CV

IAF UD@;><@HKB>S:?CF@>; A@? >S<>>F ?D> =>I<DILB>

;?I?> ;KI<> <@HKE?I?:@A @G ?D> :HKB>H>A?I?:@A š œN

^48]44^[

Z 7

Z

\ 8[

Z

8 ]4^[

Z

WD> HI:A H@F>B:AM L>A>T? @G @E= ?><DA:gE> <@H>;

G=@H ?D> IL:B:?C ?@ ;K><:GC UDI? ?D> A@H:AIB ;>=P:<>

?@ L> HI:A?I:A>F :;V F>;K:?> GIEB? @<<E==>A<>;V IAF

?@ IE?@HI?:<IBBC M>A>=I?> ?D> L>DIP:@= ?DI? HI:AJ

?I:A; ?D:; ;>=P:<>N WD> E;> @G ?D> F:;<=>?> <@A?=@BB>=

;CA?D>;:; ?><DA:gE> :; P>=C :HK@=?IA? :A @E= G=IH>J

U@=_N P>AG@=I;:HKB>F>;:MAB:_>?D>F:;?=:LE?>FI=J

L:?>=VTAF:AM IMB@LIBGIEB?J?@B>=IA<>K@B:<C:;I?=:<_C

?I;_VIAF A>>F>F ;>P>=IB ;CA?D>;:;I??>HK?;N cAF>>FV

:A ?D> K=>B:H:AI=C I??>HK?; IA IL;>A<> @G ;@BE?:@A

UI;=>K@=?>FVUD:<DUI;HI:ABC=>BI?>F?@ ?D>F>;:MA

@ABC UIC@G F>?>=H:A:AM UD>?D>= I U:AA:AM ;?=I?>MC

>S:;?;G@=I<D:>P:AMGIEB?J?@B>=IA<>N WD:;:;;E><IAA@?

L> IFF=>;;>F E;:AM ?=IF:?:@AIB H@F>B <D><_:AM ?@@B;V

I; ?D>C F@ A@? F:;?:AME:;D L>?U>>A <@A?=@BBILB> IAF

EA<@A?=@BBILB>:AKE?>P>A?;N W@?D>L>;?@G@E=_A@UBJ

>FM>V?D>@ABCIPI:BILB>H@F>B <D><_:AM?@@B ?DI?<IA

IB;@ ;@BP> ?D:; gE>;?:@A :; š œN d@U>P>=V?D:;

H@F>B <D><_:AM ?@@B @ABC <D><_; ?D> >S:;?>A<> @G I

;@BE?:@AV U:?D@E? <@A;?=E<?:AM :? >SDIE;?:P>BCV UD:B>

?D>F:;<=>?><@A?=@BB>=;CA?D>;:;LI;>FH>?D@F :;<@AJ

;?=E<?:P>N

9:;<=>?><@A?=@BB>=;CA?D>;:;>AILB>F E;?@ PIB:FI?>

I GEA<?:@AIB >S><E?ILB> ;K><:T<I?:@A LCK=@P:F:AM IA

>SDIE;?:P>;>?@G=>IB:;?:<;:HEBI?:@A ;<>AI=:@;VUD:<D

U@EBFDIP>L>>AF:e<EB??@;>?EKHIAEIBBCN >DIP>

E;>F ?D:; ?><DA:gE>I; I F>;:MA ?@@B G@= I;;>;;:AM ?D>

GIEB? ?@B>=IA? <IKIL:B:?:>; @G I M:P>A >S><E?ILB>;K><J

:T<I?:@AN b? ?D> ;K><:T<I?:@A B>P>BV ?D:; I;;>;;H>A?

:; @ABC L>DIP:@=IB¤ M:P>A :?; <E==>A? F>;:MA ;?I?>V:;

HC ;K><:T<I?:@A ILB> ?@ F>IB U:?D GIEB?;V IAF :G C>;V

D@UN WD>;CA?D>;:P>F <@A?=@BB>=IA;U>=;?D:; gE>;J

?:@AN

WD> UD@B> >SK>=:H>A?I?:@A KI=?DI; L>>A =>IB:P>F

E;:AM?D> š ›œF:;<=>?><@A?=@BB>=;CA?D>;:;?@@BV

I; U>BB I; ?D> H@F> IE?@HI?I EAF>= ?D> šœ

>AP:=@AH>A?N

6

Z 8

4

! " #$% &$'( ! $) *+,

$'$ %- $) .+% '/*'% $*% $ 0$' ( 1 .+' (*'#

*#2% %('. 3 45

678 59 :;5

6

;<=>? 0#1 @'

AB C

?B

D,E%

?

FG

H I J0#1( ! & A% ( %! .+.' ( !

#%!0K'L.*'% 3

:

;5

8MMN7O6

>

59

PQRPSTUVW?

K%0# XHY%- 4

RPZ?

FF

@ ["\ /' (?C]!? !C^_`# 'E%0

$$0#

?

D(0 *a *+%!%%() !.$$*0!'$

3 :;5

8MMN7O6

> 59 Pbc

U

Vd?2($eefgeX? FFG

e h i%* j<klmno5l

M

;<

O8M 7O p7

>m;

7q km

MN Zr>m

M

=>

h *'. \

?

FFe

X s

A

' ! t t% +# &. *'/! $02K',

$%) .% *% %- !'$.*,K * $)$*#$ u

O 95;=<m

7 5

O

Z

87MO8M

>? FGG

v s ' .+'? E _#w % !? ! E _%0 *%0a

" '#2# **'% %- #%!,0*%#* ' *% & 3

P5=x

7 l

M

; P5

O

>m;k

8 m

7 5

O

C2' (K(?Hfff

Y \ .+ !? h y%0 '?

A

y%( ? ! h A

J0 '. C) *+$'$%- !'$.*,K *.% *%$1$!

% *+ $'( K'% # *

p7

>

8

;

M m

M z{MO m

p r

O

<=

78

Zr>m

M

=| o}

M 5;r

<

ON bxxl

78

<m

7 5

O

>?

f~ea@HXg@ev

? I.,

*%1 Hfff

G ^A .'

Zr=

q 5l

78 € 5

NM l P}

M 87O6

^0D

".!#'.h01'$+$?

B

%D $$.+0$**$? FF@

F C ['2'$ &. *'/! .% *% %- !'$.* K *

$)$*#$ D'*+ 1%0 !! % 0 1%0 !! !) .%##0,

'.*'% 3 :;5

8MM N7O6

> 59 ‚Q

pz

ZUƒ„? …(%/?

C2' ?HffH

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to