Brief Announcement: Update Consistency in Partitionable Systems

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by  Matthieu Perrin

Brief Announcement: Update Consistency in
Partitionable Systems
MatthieuPerrin,AchourMoste´faoui,andClaudeJard
5 LINA–UniversityofNantes,2ruedelaHoussinie`re,44322NantesCedex3,France
1 [email protected]
0 [email protected]
2 [email protected]

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Data replication is essential to ensure reliability, availability and fault-
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tolerance of massive distributed applications over large scale systems such
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as the Internet. However, these systems are prone to partitioning, which by

] Brewer’sCAPtheorem[1]makesitimpossibletouseastrongconsistencycri-
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terionlikeatomicity.Eventualconsistency[2]guarantiesthatallreplicaseven-
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tuallyconvergetoacommonstatewhentheparticipantsstopupdating.How-
. ever,itfailstofullyspecifysharedobjectsandrequiresadditionalnon-intuitive
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c and error-prone distributed specification techniques, that must take into ac-
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countallpossibleconcurrenthistoriesofupdatestospecifythiscommonstate

1 [3].Thisapproach,thatcanleadtospecificationsascomplicatedastheimple-
v mentationsthemselves,islimitedbyamoreseriousissue.Theconcurrentspec-
5 ificationofobjectsusesthenotionofconcurrentevents.Inmessage-passingsys-
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tems,twoeventsareconcurrentiftheyareenforcedbydifferentprocessesand
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eachprocessenforceditseventbeforeitreceivedthenotificationmessagefrom
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0 the other process. In other words, the notion of concurrency depends on the
. implementation of the object, not on its specification. Consequently, the final
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0 usermaynotknowiftwoeventsareconcurrentwithoutexplicitlytrackingthe
5 messages exchanged by the processes. A specification should be independent
1 ofthesystemonwhichitisimplemented.
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We believe that an object should be totally specified by two facets: its ab-
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X stractdatatype,thatcharacterizesitssequentialexecutions,andaconsistency
r criterion, that defines how it is supposed to behave in a distributed environ-
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ment. Not only sequential specification helps repealthe problemof intention,
italsoallowstousethewellstudiedandunderstoodnotionsoflanguagesand
automata. This makes possible to applyall the tools developed for sequential
systems, from their simple definition using structures and classes to the most
advancedtechniqueslikemodelcheckingandformalverification.
Eventual consistency (EC) imposes no constraint on the convergent state,
that very few depends on the sequential specification. For example, an im-
plementation that ignores allthe updatesis eventually consistent, as allrepli-
cas converge to the initial state. We propose a new consistency criterion, up-
date consistency (UC), in which the convergent state must be obtained by a
total ordering of the updates, that contains the sequential order of each pro-
I(•1) D(•2) R{•1} Rω{•2} I(•1) D(•2) R{•1} Rω{•1,2} I(•1) D(•2) R{•1} Rω{•1}
• • • • • • • • • • • •
I(2) D(1) R∅ Rω{1} I(2) D(1) R∅ Rω{1,2} I(2) D(1) R∅ Rω{1}
(a)NotECandnotUC (b)ECbutnotUC (c)ECandUC
Fig.1:Threehistoriesforasetofintegers,withdifferentconsistencycriteria.An
eventlabeledωisrepeatedinfinitelyoften.
cess. Another equivalent way to approachit is that, if the number of updates
is finite, it is possible to remove a finite number of queries such that the re-
maining history is sequentially consistent. Unlike Fig. 1a, Fig. 1b presents an
eventuallyconsistenthistory,asbothprocessesread{1,2}oncetheyhavecon-
verged.However,itisnotupdateconsistent:inanylinearizationoftheupdates,
a deletion must appear as the last update, so this history cannot converge to
state{1,2}.State{1}ispossible becausethe updatescanbedoneinthe order
I(2),D(1),I(1),D(2), so Fig. 1c, is update consistent. As update consistency is
strictly stronger than eventualconsistency, anupdate consistent objectcan al-
waysbeusedinsteadofitseventuallyconsistentcounterpart.
We can prove that update consistency is universal, in the sense that ev-
ery object has anupdate consistent implementation in a partitionable system,
whereanynumber of crashesareallowed.The principle is tobuild a totalor-
derontheupdatesonwhichalltheparticipantsagree,andthentorewritethe
historyaposteriorisothateveryreplicaoftheobjecteventuallyreachesthestate
correspondingtothecommonsequentialhistory.Anystrategytobuildtheto-
talorderontheupdateswouldwork.Forexample,thisordercanbebuiltfrom
a timestamp made of a Lamport’sclock [4] and the id of the processthatper-
formedit.Thegenericityoftheproposedalgorithmisveryimportantbecauseit
maygiveasubstitutetocomposability.Composabilityisanimportantproperty
ofconsistencycriteriabecauseitallowstoprograminamodularway,butitis
very difficult to achieve for consistency criteria. A same algorithm that pilots
severalobjectsduringasameexecutionallowsthisexecutiontobeupdatecon-
sistent. Thisuniversalityresultallowstoimagine automatic compilationtech-
niquesthatcomposespecificationsinsteadofimplementations.
References
1. Gilbert,S.,Lynch,N.: Brewer’sconjectureandthefeasibilityofconsistent,available,
partition-tolerantwebservices. ACMSIGACTNews33(2002)51–59
2. Vogels,W.: Eventuallyconsistent. Queue6(2008)14–19
3. Burckhardt,S.,Gotsman,A.,Yang,H.,Zawirski,M.: Replicateddatatypes:specifi-
cation,verification,optimality. In:Proceedingsofthe41stannual ACMSIGPLAN-
SIGACTsymposiumonPrinciplesofprogramminglanguages,ACM(2014)271–284
4. Lamport,L.: Time,clocks,andtheorderingofeventsinadistributedsystem. Com-
municationsoftheACM21(1978)558–565