A view framework for modeling and change validation of artifact centric inter-organizational business processes

A viewframeworkformodelingandchangevalidation
of artifact-centricinter-organizationalbusinessprocesses
SiraYongchareon a, Chengfeiliu b, YuJianc, XiaohuiZhao d
a Department ofComputing,UnitecInstituteofTechnology,Auckland,NewZealand
b FacultyofScience,EngineeringandTechnology,SwinburneUniversityofTechnology,Victoria,Australia
c School ofComputerandMathematicalSciences,AucklandUniversityofTechnology,NewZealand
d Faculty ofBusiness,GovernmentandLaw,UniversityofCanberra,Canberra,Australia
a r t i c l e info
Article history:
Received27November2012
Receivedinrevisedform
13June2014
Accepted21July2014
Availableonline1August2014
Keywords:
Business processmodeling
Artifact-centric workflows
Inter-organizationalbusinessprocesses
Process views
Process abstraction
Model verification
a b s t r a c t
Over thepastseveralyears,moreefficientapproacheshavebeenonincreasingdemands
for designing,modeling,andimplementinginter-organizationalbusinessprocesses.Inthe
process collaborationacrossorganizationalboundaries,organizationsstillstayautonomic,
whichmeanseachorganizationcanfreelymodifyitsinternaloperationstomeetits
privategoalswhilesatisfyingthemutualobjectiveswithitspartners.Recently,artifact-
centric processmodelinghasbeenevidencedwithhigherflexibilityinprocessmodeling
and executionthantraditionalactivity-centricmodelingmethods.Althoughsomeefforts
havebeenputtoexploringhowartifact-centricmodelingfacilitatesthecollaboration
between organizations,theachievementisstillfarfromsatisfactionlevel,particularlyin
aspects ofprocessmodelingandvalidating.Tofillinthegaps,weproposea view
framework for modelingandvalidatingthechangesofinter-organizationalbusiness
processes. Theframeworkconsistsofanartifact-centricprocessmeta-model,publicview
constructingmechanism,andprivateviewandchangevalidatingmechanisms,which
are speciallydesignedtofacilitatetheparticipatingorganizationstocustomizetheir
internal operationswhileensuringthecorrectnessofthecollaboratingprocesses.Wealso
implementasoftwaretoolnamed Artifact-M to helporganizationstoautomatically
constructaminimalandconsistentpublicviewfromtheirprocesses.
& 2014ElsevierLtd.Allrightsreserved.
1. Introduction
Recently,service-orientedarchitecture(SOA)hasbecomea
predominantITtoolforfacilitating businessestomeetthe
changingrequirementsofthemarket.SOAparticularlyenables
thebusinesscollaborationacrossorganizationsbycomposing
Webservicestoachieveamutualbusinessgoalwithout
comprisingtheautonomyofparticipatingorganizations.The
furtherapplicationofSOAinfacilitatingbusinesscollaboration
calls forefficientapproachesfordesigning,modelingand
implementinginter-organizationalbusinessprocesses [50].
Recently,workbyDesaietal. [20], Ghattas,Montalietal.
[63] and [83] showsthatthequalityofcoordinatingorganiza-
tions inaservice-orientedcollaborationreliesonthreemajor
requirements,viz., compliance, flexibility, and autonomy.Com-
pliance requiresallpartiesmustprovidetheservicesasthey
havepromisedinthecollaborationcommitment,suchasa
servicelevelagreement. Flexibility allowseachpartytoown
thefreedomofchangingandimplementingitsownprocessin
thecollaboration.Lastly, autonomy indicateseachparticipating
organizationactsindependentlyandisnotobligedtorevealits
Contents listsavailableat ScienceDirect
journalhomepage: www.elsevier.com/locate/infosys
InformationSystems
http://dx.doi.org/10.1016/j.is.2014.07.004
0306-4379/& 2014ElsevierLtd.Allrightsreserved.
E-mail addresses: sira@maxsira.com (S. Yongchareon),
cliu@swin.edu.au (C. liu), jian.yu@aut.ac.nz (J. Yu),
xiaohui.zhao@canberra.edu.au (X. Zhao).
Information Systems47(2015)51–81

ownprivateinformation(orprocess)tootherparties.
Althoughservicechoreography definescommoncollaboration
behaviorsandkeepstheflexibilityandautonomyofeach
participant, actualchoreographymodelingapproachesand
relatedmodelinglanguagesmainlydescribethecollaboration
fromaproceduralperspective, and focusoncontrol-flow,
messagesequencing,etc.,insteadoffromadataperspective.
As such,flexibilityandautonomyisstilllimitedbythenature
of choreographymodelinglanguages.Theworkondeclarative
specificationofservicechoreographieshasbeenproposedby
Montalietal. [63], onthebasisofDecSerFlowlanguage [84],
toovercomesuchlimitationsandsupportdynamicand
complexinter-organizationalprocessspecifications.Priorto
theemergenceofservicechoreography,processviewhasbeen
adoptedtoaddresstheflexibilityandautonomyissuesin
businesscollaborations,andtheimprovementhasbeen
extensivelyevidencedinworkbyVanDerAalstandBasten
[81], LiuandShen [51,52], SchulzandOrlowska [77], Chiu
et al. [16,17], Chebbietal. [14], EshuisandGrefen [10], Zhao
et al. [100,101], Jiangetal. [40] andEshuisetal. [27].
Originally,apublic-to-privateviewapproachhasbeenintro-
duced by [85] andvanderAalstetal., [82] to resolvethe
privacyandautonomyissuesaswellastosupportchange
managementindynamiccollaboration.Mostrecently, [83]
haveproposedamultipartyprocess-orientedcontractto
supportservicechoreographybasedontheconceptsof
public/privateviewsandaccordancealongwithoperating
guidelines [61,57]. However,allofaboveworksfollowthe
traditionalactivity-centricbusinessprocessmodelingpara-
digm andtherebyinheritthelimitationsindatamanagement,
processintegration,andprocessmodification,becausetradi-
tional modelingapproacheslackadequatesupportsofauto-
matedtoolsforbusinessprocessinter-operationandprocess
schemareuse [38,39].
In thepastfewyears,anewmodelingapproachhasemer-
ged,i.e., artifact-centric (operational)businessprocessmodel-
ing [68]. Insteadofcontrolflowsofabusinessprocess,business
documentsandtheirevolutionthroughabusinessprocess
becomethemainmodelingobjects.Thisapproachdepictsa
businessprocessinfourdimensions,viz.,businessartifacts,
lifecycleofartifact,services,andassociationsbetweenartifacts
and services [34]. Thelifecycleofanartifactisdefinedinterms
of “businessstages” and thepossibleevolutionoftheartifact.
Theevolutionofanartifactandoperationsofrelatedservices
arespecifiedintermsoftheirassociations,whichcanbe
expressedinadeclarativemanner,e.g.,usingECArules.
As anemergingtoolGuard–Stage–Milestonemeta-model
is becominganewdeclarativeapproachtomodeling
artifactlifecyclebasedonavariantofstatemachines
[35,36,21,22,80]. Withtheeffortsofnumerousacademic
researchersandindustrialpractitioners,artifact-centric
modelingapproachhasbeenextensivelyrecognizedto
be withhigherlevelofrobustnessandflexibilityfordescrib-
ingprocessspecificationcomparedtotraditionalactivity-
centricapproaches.Artifact-centricprocessmodeling
receivescomprehensivecontributionsintermsofbusiness
transformationpractices [6,7,13], foundations [5,59], design
methodologies [8,19,56,64,65,73,74,86], modelspecifica-
tion,construction,andverification [54,30,31,44,25,29,102,
103,21], workflowrealization/execution [18,53,66,91,67,88],
and monitoring/conformancesupports [55,28]. Uptopresent,
artifact-centric approachhasbeenappliedtoseveralindus-
try domainssuchas healthcare (e.g., PHILharmonicFlows
framework [45,15]), insurance (e.g., in [44]), and finance (e.
g., IBMGlobalFinancing [13]). However,comparedwith
traditionalactivity-centricapproaches,furtherresearchis
sought afterintheareaofbusinesscollaboration.
By nowtwomainapproacheshavebeenproposedfor
artifact-centricinter-organizationalprocesses. Theinitial
attempt usesartifact-centricinteroperationhubtofacilitate
and supportinter-organizationalworkflows(inanorchestra-
tion perspective)amongmultipleautonomousstakeholders
[37]. Recently,thisworkhasbeenbroughtforwardtoanEU-
funded projectcalledArtifact-CentricServiceInteroperation
(ACSI) [3]. Itispromisedtosupportalargenumberofservice
collaborationbyusingartifact-centricinter-operationsandto
achievedramaticsavingsoverconventionalapproaches.On
the otherhand,theartifact-centricchoreographyapproach
hasdefinedinteractingartifact-centricprocesses [58,79].
Althoughflexibilityisnaturallydeemedasoneofthebenefits
fromartifact-centricmodelingapproaches,acomprehensive
studyonsupportingorganizationstoachieveallthethree
collaborationrequirementsisstillmissing.Basedonliterature
andpractices,wehaveobservedthatview-basedapproaches
tointer-organizationalbusinessprocessmanagementcan
provideapromisingandefficientwayofprocessmodeling
and changemanagementtoaddresssuchrequirements;
nevertheless,ithasnotbeenyetmuchexploredinthecontext
of artifact-centricinter-organizational businessprocesses.
Therefore,inthisarticle,wearetoexploretheideaofprocess
viewinanartifact-centricperspectiveanddevelopaframe-
workthatcanhelporganizationstomeettheaforementioned
requirementsinacollaboration environment.Wesummarize
our contributionsasfollows:
Weproposeaformalartifact-centricviewframework
based onLTS(LabeledTransitionSystem).Thisframe-
workconsistsofthreeparts:(1)anartifact-centricMeta
model forinter-organizationalbusinessprocesses,(2)
notion of privateview for capturinglocalprocessesof
participating organizations,and(3)notionof public view
for servingasanagreedcontractofthecollaboration.
With public/privateviews,organizationsareableto
autonomouslyparticipateinthecollaborationwhile
being freetochangetheirlocalprocesses.
Wedesignanalgorithmforautomaticallyconstructinga
consistent,minimalpublicviewbasedonlocalpro-
cesses ofanorganization.Tothebestofourknowledge,
this isthefirstalgorithmforautomaticallyconstructing
a collaborationcontractthattakesintoaccountinterac-
tion behaviorsofartifacts.
Wedevelopaverificationmechanismforartifact-centric
processesthatallowsorganizationstochangetheirlocal
processes,throughtheuseofprivateviews,while
preservingthecorrectnessandconsistencyoftheover-
all collaboration.Astheverificationisperformedlocally,
our mechanismdoesnotsufferfromthestateexplosion
issue thatmayoccuringlobalverificationapproaches.
The remainderofthisarticleisorganizedasfollows:
Section 2 introducesthemotivationofourartifact-centric
52 S. Yongchareonetal./InformationSystems47(2015)51–81

approachandtheconceptofprocessviews. Section 3
presentsourviewframeworkforartifact-centricbusiness
processes. Sections 4 and 5 address howtocreatepublic
viewsandprivateviewsaswellashowtoensureview
consistencyandvalidatelocalprocesschanges,respec-
tively. Section 6 discusses animplementedprototypefor
the proof-of-conceptpurpose. Section 7 reviewstherelated
work.Finally,conclusionandfutureworkaregivenin
Section 8.
2. Motivatingexample
In thissection,weuseapurchasingprocessinthesupply
chaincollaborationdomainasanexampletoillustrateand
motivatetheartifact-centricapproachtomodelinginter-
organizationalbusinessprocesscollaboration.In Fig.1, a
completepurchasingprocessmodelinthecollaborationis
illustratedbasedonanartifact-centricperspective,which
involvesthreerolesofparticipatingorganizations: Buyer,
Supplier, and Logistics. Weinitiatethediscussionofthis
examplebyidentifyinginvolvedbusinessartifactsand
describinghowtheyaremodeledinthiscollaboration.
At thebeginningstage,allpartiesidentifyandmodel
their requiredbusinessartifactsoftheirlocalprocesses.
This stepincludesdefiningorganization-ownedartifacts
(called local artifacts) thatareinternallyused/managedby
individualpartyaswellastheircommonlyagreedartifacts
(called sharedartifacts) thatareusedforthecoordination
betweenpartiesinthecollaboration.Weconsiderthatthe
lifecycleofasharedartifactshouldrepresentitsagreed
business stagesandpossiblestepstowardsthecompletion
of theprocess.Inotherwords,sharedartifactsshouldbe
used asamutualpointofinterestofallparties;therefore,
the coordinationoccursatsomepointswheretheyare
processed.Intheimplementation,thesesharedartifactsact
as messagesthataresentandreceivedbytheseorganiza-
tions. Baseduponthecurrentprocessingstateoftheshared
artifact, aresponsibleorganizationthathasreceivedthis
artifact willinvokeaspecificserviceaccordingtoacorre-
sponding businessruledefinedbythatorganization.This
service willthenreadorupdatethesharedartifactand
otherlocalartifactsdefinedinthespecification.
In Fig. 1, wecanseethattheinter-organizationalprocess
consists of PurchaseOrder (PO), Shipping Order (SO), and
Invoice (IV) as sharedartifacts. Apartfromthem,Buyer,
Supplier,andLogisticshave Quote (Q) and Payment (P),
Picking List (PL) and DeliveryNote (DN), and Shipping List
(SL) astheir local artifacts, respectively.Inthefigure,we
also usedashedlinetodepictthe synchronizationdepen-
dencies betweenartifacts(local-local,shared-shared,or
local-shared).
Nextwebrieflydescribetheprocessin Fig. 1 from an
artifact-centric perspective.Atthebeginningoftheprocess,
a buyerinitiatesthecreationofthe Quote and the PO
documents/artifacts. Oncethe quote is approved,the PO is
confirmed andsenttoaselectedsupplier.Whenthe
supplier receivesthe PO, itcreatesa PL document forthe
purpose ofacquiringgoodsforthat PO. Ifthegoodsrunout,
then thesupplierrejectstosupplythemandthencancels
the PO. Otherwise,thegoodsarefilled,andthenthe
supplier generatesaninternal DN document andcreatesa
SO document forthedesignatelogisticscompany.Oncethe
SO is received,thelogisticscompanycreatesa SL document
that isusedforpickingupthegoodsfromthesupplier’s
shipping pointandalsodeliversthegoodstothebuyer.
Afterthat,thesuppliercreatesan IV document andsendsit
to thebuyer.Sometimelater,thebuyerclearsthetotal
amount owinginthe IV, consequently,thesuppliermarks
the PO as closed.Thispurchasingprocesscompleteswhen
Buyer (L1) Supplier (L2) Logistics(L3)
Purchase Order(PO)
Picking List(PL)
ready tofill Filled order
checking
Quote (Q)
created approving
approved
In stock
Shipping Order(SO)
In transit
arrived
Invoice (IV)
cleared
Shipping List(SL)
Queued
completed picked
created confirmed
L1
closed
L2 billing L2
canceled
accepted filled
acquiring
L2
L2
delivering
L2
ready toship
L2
L3
created
L2
L2
Out ofstock
L2
L1
sent issued
L2
L2
Payment (P)
approving created
sent
Delivery Note(DN)
prepared
transferring
L3
scheduled
dispatched
L3
unpaid
L1
L1
rejected
L1 on hold
L1
clearing
L2
Fig. 1. A completeartifact-centricinter-organizationalpurchasingprocess
S. Yongchareonetal./InformationSystems47(2015)51–81 53

the PO is inthe closed state, the SO is inthe arrived state,
and the IV is inthe cleared state.
In thecontextofinter-organizationalprocesscollabora-
tion, someconcerns—including changeflexibility,change
verification,andprivacy—raisedinthetraditionalactivity-
centric approach(e.g.,in [85,32]) shouldalsobeconsidered
in anartifact-centricsettingasdiscussedbelow.
First, organizationsprefertokeepthe freedom of mod-
ifying theirinternalprocesseswithoutrevealingtheirlocal
changestootherparticipatingparties.Inotherword,once
they haveagreedontheoverallprocess,theyshouldhave,
possibly,thehighestlevelof flexibility tomodifytheirown
local processeswhileremaining autonomous in thecolla-
boration [85,82,83]. Forexample,Suppliermaymodify
some processingstepsofits PL artifact, andsuchchange
should notbeexposedtoBuyerandLogistics.Apartfrom
the changeofexistinglocalartifacts,theyshouldbe
allowedtoaddnewlocalartifactstotheirprocesscaused
by processexpansion/improvement.Forinstance,Supplier
may needtoincorporate InventoryList (IL), whichisused
for inventorymanagement,totheirprocess.The IL artifact
needs tointeractwithexistinglocalartifact PL. Italso
implies that IL indirectlycontributestothepartofshared
artifact PO through PL. Inordertosupportthechangeof
local processes,organizationsneedtoknowwhatthey
wanttomodifyandhowsuchmodificationcanbeapplied.
Second, stemmedfromthefirstreason,thechangeto
anylocalprocessshouldnotaffectthebehaviorofthe
overallcollaboration.Thisimpliesthatalocalprocess
should always comply with thecontractagreedbyall
parties, andthechangemadetolocalprocessesshould
not affecttheoverallprocess.Therefore,allpartiesmust
ensure thattheirlocalchangesdonotviolatethecollabora-
tion contract.Forexample,ifSupplierchangestheir PL
artifact byremovingatransition ready_to_f ill-f illed_
order, thenthismayaffectthetransition acquiring-f
illed of PO; consequently,Logisticsisnotabledetermine
whether thegoodsarereadytobepickedfordelivery.In
addition, allparticipatingpartiesshouldalsobeawareof
the localchangesthatwillpropagateandeventuallyaffect
the overallprocess.Forinstance,iftherearesomechanges
made on IL artifact, thentheydirectlyaffectthe PL artifact
and eventuallyaffectthe PO artifact. Thisraisestheissueof
how wecanguaranteethatlocalchangesmadebyan
individualpartydonotleadtoincorrectbehaviorofthe
overallcollaboration.Inotherwords,organizationsmust
ensure thatchangesintheirlocalprocessesarein compli-
ance with whattheyhavepromisedtoprovide.
Last, organizationsconcernabouttheir privacy. Inthe
collaboration,itisnecessaryfortheparticipatingorganiza-
tions torevealcertaindetailsoftheirinternalprocesses
among themselvesatanadequatelevelofvisibilityasto
establish anoverallpictureofthecollaboration,whichis
used asaprocessagreementorcontractamongthem.In
our artifact-centricinter-organizationalprocessmodeling
approach,thelevelofvisibilitycanbedeterminedbasedon
the typeofartifacts.Inotherwords,detailsoflocalartifacts
should bekeptinvisibletoexternalpartiesasmuchas
possible whiletheyalsosupporttheoverallprocessby
means ofdependencyassociationswithsomeprocessing
part (lifecycle)ofthesharedartifact(s).Considerthe DN
artifact in Fig. 1 for instance.The DN is privatelyusedby
Supplier;however,wecanseethatithasdependency
associations withthesub-lifecyclesofthe PO (f illed-ready_
to_ship-dispatched) and SO (-created-scheduled-
in_transit), whicharesharedartifacts.Simi-
larly,both Quote and PL artifacts areusedtosupportsome
processingstepsofthe PO artifact. Toachieveprivacy,ifa
processingstepofasharedartifactisexclusivelycontrolled
by thelocalartifact(s)ofoneparty,thenthatstepshould
notbevisibletootherparties.Forexample,the ready_
to_ship state anditsrelatedtransitionsof PO should bekept
invisibletoexternalpartiesbecause DN is alocalartifact
of Supplier.Apartfromthat,wecanseethatthestep
created-scheduled of SO can behiddentoexternalparties
as well.Inordertosupporttheprivacyrequirement,an
organization needstohaveamechanismtoidentifyan
artifact and/oritspartsthatcanbeinvisibletotheother
parties. Thisbringsupinthequestionoftowhatextentofa
local processcanbekeptprivatewhilenotaffectingthe
successful establishmentofthecollaboration.
The threemajorconcernsdiscussedabovecallforan
approachtoefficientmodelingandchangemanagementof
artifact-centric inter-organizationalbusinessprocesses.As
previouslydiscussed,inthisarticle,westudyhoworgani-
zations canapplytheconceptof view to supportand
facilitatethemodelingoftheircollaboratingbusiness
processesinanartifact-centricparadigm.Particularly,we
borrowtheideaofpublicandprivateviewsapproachto
inter-organizationalworkflowswhichisoriginallystudied
in activity-centricbusinessprocessmodelingapproaches
[85,82,83], andthenexploreitinthecontextofartifact-
centric processes.
3. Viewframeworkforartifact-centricinter-
organizationalprocesses
In thissection,weintroduceanddiscussourview
frameworkforartifact-centricinter-organizationalbusiness
processes.In Section 3.1, weoverviewourviewframework
that aimsataddressingtheaforementionedrequirements
for efficientinter-organizationalbusinessprocessescolla-
boration.Thenin Section 3.2, weformallydefinetheview
frameworkanddiscusshowtouseittomodelinter-
organizational businessprocessesfollowedbythediscus-
sion ofbehaviorpropertiesin Section 3.3.
3.1.Overview
Westartthissectionbyintroducingourviewframe-
workformodelingartifact-centricinter-organizational
business processes-whichisinfluencedbytheprocess-
orientedcontractapproachproposedforservicechoreo-
graphy [83]. Ourartifact-centricviewframeworkconsists
of thefollowingfourparts:(1)Artifact-Centricbusiness
Processmodelforinter-organizationalbusinessprocesses
(ACP-imodel), (2)publicviewanditsconstructionmethod,
(3) processchangemechanism,and(4)processchange
validation. Fig. 2 depicts theoverallpictureoftheframe-
workbytakingourmotivatingpurchasingprocessesasan
illustrativeexample.

Our viewframeworkisdevelopedbasedonthenotion
of privateview and public view proposedby [85]. A private
view is usedtocapturethe local processes of eachindividual
organization, whilea public view of aparticularcollabora-
tion processisan abstract representationoftheoverall
processthatisnecessaryforthecoordinationandhidesthe
details oftheprivateprocessesofeachorganizationas
much aspossible.Organizationscanachieveanefficient
collaboration(regardingthethreerequirements)basedon
the public–privateviewsapproachbythefollowingfour
stepsasillustratedin Fig. 2.
(1) Constructacompleteartifact-centricmodelspecifica-
tion ofinter-organizationalbusinessprocess
(2) Createa public view that isservedasamutualagree-
ment, i.e.,contract,ofthecollaboration.
(3) Eachorganizationcanchangeandvalidatetheirlocal
processes,viatheuseof privateview, withouttheneed
for globalverification.
First, allparticipatingpartiesspecifyacompletespeci-
fication oftheirinter-organizationalbusinessprocessasto
achievetheirgoalofthecollaboration.Aspreviouslydis-
cussed, thecoordinationamongthemcanbespecifiedby
defining allsharedartifactsandtheirinteractionswithlocal
artifacts (fromeachparty).WecalltheArtifact-Centric
Processmodelofthecompleteinter-organizationalprocess
an ACP-imodel. Onceallparticipatingorganizationshave
agreedonthecompletemodeloftheartifact-centric
collaborationprocess,theyconstructanagreedpublicview
of suchprocess.Thispublicviewrevealsonlythenecessary
information ofartifactsthatisrequiredtobeusedforthe
coordinationamongparties.Intheperspectiveofartifact-
centric processmodeling,apublicviewshouldonlycontain
sharedartifacts and shouldnotrevealanylocalartifactor
the partofasharedartifactthatissupportedbylocal
artifact(s).
Once thepublicviewisbuiltasacontract,each
participating partyhastheresponsibilitytoensurethat
its localprocesses(i.e.,responsiblepartsofsharedartifacts
and theirlocalartifacts)canprovidewhathasbeen
specified inthecontracttootherpartiesinvolvedinthe
collaboration.Themostimportantthingsareasfollows:(1)
the constructedpublicviewmustbesoundandconsistent
with itsbaseprocess;and,(2)whenanorganization
modifies itsownpartsofbothtypesofartifactsusedin
the collaboration,itmustguaranteethatsuchlocalchanges
do notcompromisethecorrectnessoftheoverallcollabora-
tion. Wewilldiscusstheconstructionofapublicviewand
changemanagementinalocalprocessindetailin Section 4
and 5.
3.2. SyntaxforACP-imodel
Here,weformallydefinetheartifact-centricprocess
model forinter-organizationalbusinessprocesses,or ACP-i
model, whichisanextendedversionoftheACPmodel
presentedinourpreviousworks [97,98,95,96,94]. An ACP-i
model consistsoffourmaincomponents: roles, artifacts, tasks,
and businessrules.Roles defineasetofparticipatingorganiza-
tionrolesinthecollaboration.An artifact isabusinessentity
or anobjectinvolvedininter-organizationalbusinesspro-
cesses. A task is ownedbyoneorganizationinthecollabora-
tionandisusedtoperformread/updateoperationsonartifact
(s).A business rule is definedbyafamilyofconstraintsin
a Condition-Action styletodescribewhichserviceisin-
vokedandwhichstateofanartifactischangedunderwhat
condition.
Definition 1. (Artifact class).Anartifactclassabstractsa
group ofbusinessartifactswiththeirattributesandstates.
Artifact classC (or artifact if thecontextisclear)isatuple
(A; S; sinit ; Sf ) where,
A ¼ fa1; a2; …; axg; aiAAð1rirxÞ is aname-value
pairedattributevariable,
S ¼ fs1; s2; …; syg; siASð1riryÞ is astate,
sinit =2 S denotesthepseudoinitialstate,
Sf S is asetoffinalstates.
ACP-i
ACP ACP ACP
ACP-i (modified)
ACP ACP ACP
PUBLIC VIEW
pa(ACP-i)
private viewchangevalidation
public viewconstruction 2
4
inter-org processconstruction 1
changes inlocalprocesses
Purchase Order
Shipping Order
Invoice
Buyer Supplier Logistics
Picking List Quote
Shipping List
Payment
Deliver Note 3
′
Fig. 2. Our viewframeworkforartifact-centricinter-organizationalbusinessprocesses.

Definition 2. (Artifact schema).An artifactschema,
denotedas Z, containsasetofartifactclasses,i.e., Z ¼
fC1; C2; :::; Cxg where CiAZð1rirxÞ is anartifactclass.
Wealsodefinesomebasicpredicatesoverschema Z to be
used fordefiningbusinessrulesasfollows:
def inedðC; aÞ iff attribute aAC:A of artifactofclass C is
defined;
instateðC; sÞ iff state sAC:S of artifactofclass C is active.
Next,wedefineabusinessruletoexpressthecontrol
logic ofabusinessprocess.
Definition 3. (Business Rule).Abusinessruleregulates
which taskcanbeinvokedunderwhatpre-condition.The
conditional effectisalsodefinedtowhatpost-condition
needs tobesatisfiedafterperformingsuchtask. Business
rule r is triple ðλ; β; vÞ where
λ and β are thepre-conditionandthepost-condition,
respectively.Bothconditionsmaycontainthefollowing
twotypesofpropositionsoverschema Z: (1)state
proposition(the instate predicate)and(2)attribute
proposition(the def ined predicate).Tomakethetarget
statedecidable,wedonotallowthepost-conditionto
include disjunctioninstatepropositions.
vAV is ataskoracompositetask(i.e.,morethanone
atomictask); V ¼ fv1; v2; :::; vxg is asetoftasksof
which performsoperationsonsomeartifacts C1, C2,…,
Cy where CjAZð1rjryÞ.
In ordertomaintaintheexistenceofvalidandexplicit
state changesofanartifactinbusinessrule r, werequire
that thereexistsacoupleof instate predicatesofthat
artifact inboththepre-conditionandthepost-condition
of r, i.e.,wehavestates sx; syAC:S such that instateðC; sxÞ
existsin r:λ and instateðC; syÞ existsin r:β. Thestatechange
referstoeitheratransitionfromonestatetoanotherstate,
or toitself. Table1 lists somebusinessrulesusedinour
purchasingprocessin Fig. 1.
Wealsoclassifybusinessrulesintotwotypesbasedon
the existenceofthe instate predicateinthepre-andpost-
conditions ofabusinessrule.Thefirsttypeonlychanges
the stateofonesingleartifact,whilethesecondtype
simultaneouslychangesthestatesofmultipleartifacts,i.
e., morethanonepairof instate predicates(onepairforone
artifact) mustappearinthepre-andpost-conditionsofa
single businessrule.Wecallthesecondtype synchroniza-
tion (sync)rules as theyareusedforexpressingsynchroni-
zation betweenartifacts.
Definition 4. (Sync rule).Businessrule r is a sync rule for
artifact Cx and artifact Cy if thereexists instate ðCx ; siÞ and
instate ðCy ; smÞ in r. and instateðCx ; sjÞ and instateðCy ; snÞ in
r:β, where si; sjACx:S and sm; snACy:S.
As mentionedabove,asingle sync rule can beusedto
synchronizemorethantwoartifacts.
Example 1. In Table1, wecanseethatbusinessrules r2 is
used toexpressonlythestatechangeofthe PO artifact
(conf irmed-accepted), whilebusiness(sync)rule r1 is used
tosimultaneouslychangestatesoflocalartifact Quote
(approving-approvedÞ and sharedartifact PO (on_hold-conf
irmedÞ. Similarly,business(sync)rule r3 is usedforthe
synchronizationof DN and SO; andsyncrule r4 is usedfor
synchronizingfourartifacts PO, DN, SO, and IV (wheretwo
tasks aredefinedinitsaction).
Next,wedefine ACP-i model to capturethecomplete
specification ofaparticularinter-organizationalbusiness
processinthecollaboration.Asdiscussedin Section 2,
sharedartifactsshouldbeusedascoordinationmeansin
inter-organizationalbusinessprocesses.However,ashared
artifact cannotbecompletelymodeledsolelybyasingle
Table1
An exampleofbusinessrulesforourpurchasingprocess.
r1: Buyerapproves Quote q to confirm PurchaseOrderpo for aselectedsupplier
Pre-condition instate(q, approving) 4 instate(po, on_hold) 4 defined(po,OrderID) 4 defined(po.SupplierID)
Task approve(q,po)
Post-condition instate(q, approved) 4 instate(po, confirmed) 4 defined(po.SubmitDate)
r2: Supplier accepts PurchaseOrderpo
Pre-condition instate(po, confirmed) 4 defined(po,OrderID) 4 defined(po.SupplierID)
Task acceptPO(po)
Post-condition instate(po, accepted)
r3: Supplier creates Shipping Orderso from DeliveryNotedn
Pre-condition instate(dn, prepared) 4 defined(dn.ShipperID) 4 instate(so, init)
Task createShipping (dn,so)
Post-condition instate(dn, transferring) 4 instate(so, created) 4 defined(so.ShippingID)
r4: Supplier dispatchesgoodsfor PurchaseOrderpo that tobeshippedby Shipping Orderso,
and simultaneouslyissues Invoiceiv to theBuyer
Pre-condition instate(po, ready_to_ship) 4 instate(dn, transferring) 4 instate(so, scheduled) 4 instate(iv,init)
Task dispatchGoods(po, dn,so)issueInvoie(po,iv)
Post-condition instate(po, delivering) 4 instate(dn, dispatched) 4 instate(so, in_transit) 4 instate(iv,issued)
4 defined(iv.InvoiceID) 4 defined(iv.OrderID)

organization duetoitssharingnature.Therefore,allparti-
cipating organizationsmustagreeonboththestructure
(data model)andthebehavior(lifecycle)oftheshared
artifacts inordertodefinetheACP-imodel.Itisworth
noting thatinordertomaintaintheintegrityofashared
artifact togetherwithalltheinvolvedtasksandbusiness,
we assumethatthenameofitsstateandattributemustbe
uniquelyidentifiedforthesamemeanacrosscollaborating
organizations.
Definition 5. (Organization Role).Wedenote L ¼
fl1; l2; …; lxg for asetof organization roles, where
liALð1ixÞ is aroleoforganizationsthatparticipateinan
inter-organizationalbusinessprocess.
Definition 6. (ACP-imodel).Givenasetoforganization
roles Linvolvedinacollaboration,wedefinean ACP-i
model, denotedas Π^ ¼ ðZ; V; R; L; γÞ, fortheirinter-
organizational businessprocesswhere
Z is anartifactschema, V is asetoftasks,and R is asetof
business rules,
L is asetofparticipatingorganizationroles,
γ: Z [ V [ R-2L is arolemappingfunctionfroman
artifact class,abusinessrule,orataskontoanorganiza-
tion role(s)asfollows:
(c) γðCÞ returnsasetofroles fl1; l2; …; lxg, where
liALð1rirxÞ is arolethatcanaccess(read/write)
artifact CAZ and theownerof C must beamong
roles γðCÞ. Notethata sharedartifactC implies that
jγðCÞj41, andif C is a local artifact then jγðCÞj ¼ 1.
(c) γðvÞ returnsrole lAL of organizationwhoownstask
vAV. Notethatataskcanperformread/write
operationsoneitherlocalartifactorsharedartifact
or both.
(c) γðrÞ returnsrole lAL of organizationwhoowns
business rule rAR.
In addition,wedefinetwoauxiliaryfunctionsover
business rules R and artifactschema Z in Π^
function pre_sðr; CÞ returnsasetofstates{s1; s2; :::; sxg
whereforsomebusinessrule rAR, state
siAC:Sð1rirxÞ occurs inatleastone instate predicate
of thepre-conditionof r; and,
function post_sðr; CÞ returnsasetofstatesofartifact C
appearing inthepost-conditionof r.
Givenan ACP-i model, wecanderivealocalACPmodel
for anorganization'slocalprocess.Notethatinalocal
processofanorganization,theattributesandstatesofits
sharedartifactcanbeobtainedfromthe ACP-i model if they
arespecifiedinthebusinessrulesoflocalprocess.
Definition 7. (local ACPmodel).Given Π^ ¼ ðZ; V; R; L; γÞ be an ACP-imodel, alocalACPmodelofrole lAL can be
derivedfrom Π^ , whichisdefinedas Π^ l
¼ ðZl; Vl; Rl
Þ where,
Zl
¼ fCAZ j lAγðCÞg is alocalartifactschema,suchthat
each sharedartifact in Zl contains astate s if andonlyif
instateðsÞ appears inthepre-orpost-conditionofa
business rulein Rl, i.e.,
8CAfCAZl
j lAγðCÞ 4 γðCÞ

41g; 8sAC:S; (rARl;
sApre_sðr; CÞ [ post_sðr; CÞ;
Vl
¼ fvAV j γðvÞ ¼ lg is asetoflocaltasks,
Rl
¼ frAZ j γðrÞ ¼ lg is asetoflocalbusinessrules.
Example 2. Fig. 3 showstheSupplier'slocalACPmodel
which isderivedfromthe ACP-i model of thepurchasing
processillustratedin Fig. 1. Wecanseethattheshared
artifacts PO and SO representonlythepartsthatbelongto
the Supplier'slocalprocess,e.g.,someprocessingstepsof
PO (beforethe confirm state)and SO (after the in_transit
state) thatbelongtoBuyerandLogistics,respectively,are
not capturedintheSupplier’s localACPmodel.
Next,wediscussthebehaviorpropertiesofartifact-
centric inter-organizationalbusinessprocesses.Ingeneral,
it isimportantthatthebehaviorofinter-organizational
business processesmustbesoundinordertoguaranteethe
reachabilityofdesiredgoalsofthecollaborationand
participating localprocesses [83,58,42].
3.3. BehaviorpropertiesofACPmodelanditsartifacts
Weclassifybehavioralpropertiesofartifactsin ACP-i
model into intra-behavior and inter-behavior. Theintra-
behaviorofanartifactdescribeshowanartifactchanges
its statethroughoutitslifecycle.Here,weadoptLabel
TransitionSystem(LTS)tocapturethelifecycleofan
individualartifact.Second,theinter-behaviordescribes
how thelifecycleofoneartifactdependsonthecounter-
part ofanotherartifact,anditcanberepresentedas
synchronizationdependencybetweenartifacts,i.e.,a sync
rule.
Here, wegeneralize ACP-i model Π^ to ACPmodel,
denotedas Π¼ ðZ; V; RÞ, bydisregardingtherolesoforga-
nizations androlemappingof Π^ .
Definition 8. (Lifecycleofartifact, )n). Let
Ci ¼ ðAi; sinit
i ; Si; Sf
i Þbe anartifactclassin ACPmodel Π.
Picking List(PL)
Purchase Order(PO)
confirmed
acquiring
accepted filled
canceled
checking In stock
Out ofstock
delivering
ready toship
Delivery Note(DN)
prepared
transferring
dispatched
closed billing
Shipping Order(SO)
In transit created scheduled
Invoice (IV)
cleared
sent issued
unpaid
clearing
Fig. 3. A localACPmodelforSupplier.

A lifecycle of Ci, denotedas ℒCi , canbedefinedasatuple
ðS; sinit ; )Þ where,
set ofstates S ¼ Si, initialstate sinit ¼ sinit
i ,
statetransitionrelation ) DS Ri Gi S where
RiD Π:R is asetbusinessrulesthatareusedtoinduce
statetransitionsofartifact Ci such that,
8rAΠ:R; (sx; syACi:S; sxApre_sðr; CiÞ 4sy
Apost_sðr; CiÞ-rARi;
Gi (guards)isaunionsetofstatepreconditionsofeach
business rulein Ri such thateachpreconditionrefer-
ences toastateofotherartifactin Π, i.e.,
Gi¼ [jΠ:Zj j ¼ 1 fCj:sj(rARi; (CjAΠ:Z; sApre_sðr; CjÞ4CjaCig ;
Wealsodenote )n for areflexivetransitiveclosureof
). Wewrite si)nsj if state sj can bereachedfromstate
si by somesequenceofbusinessrulesin Π:R.
Wewritetransition ss)
r½gst tomeanthatthestateofthe
artifact willchangefromsourcestate ss totargetstate st if
business rule r is firedandguard g (state pre-conditionof r)
holds. Notethatinaclearcontext,wemayuseshorthand
ss ) st without itssuperscription,andmayuseterm
artifact for themeanof lifecycleofartifact.
Based on Definition 8, given ACPmodelΠ, wecanderive
a lifecyclecorrespondingtoanartifactin Π from asetof
correspondingbusinessrulesthatareusedtotriggerthe
state transitionsoftheartifact.Wecanobtainthelifecycle
of anentireprocessbycomposingallartifactsinthemodel.
Here, wedefine ACPlifecycle for describingthebehavioral
aspect ofanACPmodelconsistingofsynchronizedlife-
cyclesofartifacts.Weadaptastatemachinecomposition
techniquepresentedin [49] for generatingthelifecycleof
ACP.Similartechniqueforprocessmodelgenerationbased
on (object)lifecyclecompositionisalsopresentin [46].
Definition 9. (Lifecyclecomposition,composedlifecycle,
). Let ℒi ¼ ðSi; sinit
i ; )iÞ, and ℒj ¼ ðSj; sinit
j ;)jÞ be two
artifact lifecyclesinACPmodel Π. Lifecyclecomposition
(i.e., synchronizedproduct)of ℒi and ℒj is denotedas
ℒc ¼ℒi ℒj ¼ ðSc; sinit
c ;)cÞ where,
ScDℒi:S ℒj:S is asetofcomposedstates,
sinit
c ¼ ðℒi:sinit ;ℒj:sinit Þ is theinitialstate,
—)cD Sc Π:R Gc Sc is atransitionrelationwhere Gc is a
set ofguards(statepropositions).
Now,let g½sx
ℒi=stateðℒi; sxÞ denotethatstate sx
ℒi in
guard g is substituted (denotedbysymbol/)by true or
f alse (of statepredicate)dependingonwhetherthelocal
stateof ℒi is sx. Wecanformulatetransitionrelation )c of
composedlifecycle ℒc , byusingthefollowingthreeinfer-
ence rules.
ðsx
ℒi ; r; g1; sy
ℒi ÞA)i
ððsx
ℒi ; sx
ℒj Þ; r; gc; ðsy
ℒi ; sx
ℒj ÞÞA)c; gc ¼ g1½sx
ℒj=stateðℒj; sxÞ
ð3:1Þ
ðsx
ℒj ; r; g2; sy
ℒj ÞA)j
ððsx
ℒi ; sx
ℒj Þ; r; gc; ðsx
ℒi ; sy
ℒi=stateðℒi; sxÞ
ð3:2Þ
ðsx
ℒi ; r; g1; sy
ℒi ÞA)i4ðsx
ℒj ; r; g2; sy
ℒj ÞA)j
ððsx
ℒi ; sx
ℒj Þ; r; gc; ðsy
ℒi ; sy
ℒj=stateðℒj; sxÞ 4g2ðsx
ℒi=stateðℒi; sxÞÞ
ð3:3Þ
Rule (3.1) and Rule (3.2) are appliedwhenbusinessrule r is
firedononlyindividuallifecycle ℒi and ℒj, respectively.
Rule (3.3) is appliedwhen sync ruler is firedonboth
lifecycles ℒi and ℒj. Asthethreeinferencerulesapply
the substitutionofstateconditionsoftwolifecyclesinthe
composition, referencestoexternallifecyclearenot
replaced.
Example 3. Fig. 4 showsthecompositionbetweenthe
lifecycleofartifact C1 and thelifecycleofartifact C2. The
label ri½g attached toatransitionmeansthatthetransition
is firedwhenboththeattributepropositioninthepre-
condition ofbusinessrule ri holds andallstatepropositions
(of externallifecycles)in g hold. Wedenotethecounter
stateconditionof C:sx by symbol C:sx in theguard.We
can alsoseethatstateconditionsreferencingtoartifacts C3
and C4 remaininthecomposedlifecyclebutindifferent
forms, whichdependonthetransitiontheybelong.
Now,wecandefinethelifecycleofACPbyusing lifecycle
composition.
Definition 10. (ACPlifecycle).GivenACPmodel Π, a (ACP)
lifecycle of Π, denotedas ℒΠ, canbegeneratedbyitera-
tivelyperforming lifecyclecomposition of everyartifactin
Π.
Notethat lifecyclecomposition is associativeandcom-
mutative,i.e., ℒi ℒj ℒk ¼ ℒi ðℒj ℒkÞ ¼ ðℒi
ℒjÞ ℒk and ℒi ℒj ¼ℒj ℒi. Therefore,thefinal
resultofthecompositionofasetoflifecyclesisnot
impactedbytheircompositionorder.
Next,wedefine soundness propertytodescribeadesired
and correctbehaviorofartifactlifecycleandtheprocess.
Definition 11. (Safe, goal-reachable,andsoundlifecycle).
GivenACPmodel Π and lifecycle ℒ¼ ðS; sinit ; )Þ, we
Fig. 4. An exampleoflifecyclecomposition(takenfrom [96]).

define asetoflifecyclestates S ¼ ℒ:S [ fsinitg and asetof
final states Sf S. Lifecycle ℒ is saidtobe:
safe iff thereexistsbusinessrule rAΠ:R such that r
induces oneandonlyonetransitionin ℒ, i.e.,
Π:R; ðsx; r; g; syÞA
) ðsm; r; g; snÞ=2 )
goal-reachable iff, foreverynon-finalstate s of ℒ, s can
be reachedfromtheinitialstateand s can reachoneof
the finalstatesof ℒ, i.e.,
8sAS Sf ; (sf ASf ; sinit) n
s s) n
sf
sound iff ℒ is safe and goal-reachable.
Notethatthe goal-reachability propertyimplies
deadlock-freeandconnectedlifecycleofanartifact(ora
process).
Nowconsiderthecaseofasharedartifactdefinedina
local ACPmodel.ItisalwaystruethatthelocalACPmodel
is not goal-reachable as thelifecycleofsharedartifactis
partially modeledandcanbenon-terminated.However,
when integratingallthedifferentpartsofasharedartifact
from eachorganization,thecompletelifecyclemustbe
goal-reachable.
In thisarticle,wedonotfocusonthetask-level
information, i.e.,thespecificationoftaskisomitted.How-
ever,thespecificationoftaskinartifact-centricprocess
modeling approachcanbedefinedinthespiritofsematic
web-servicesspecifiedinOWL-Sproposal[2003]—that isin
a formofInput,Output,Pre-condition,andEffect(IOPE).
The pre-conditionandconditionaleffectofataskshould
conform tothepre-conditionandpost-condition,respec-
tively,ofthebusinessrulethatspecifiesthetaskinits
action. Adetaileddiscussionofsemanticweb-services
togetherwiththeuseofbusinessrules(e.g.,SBVR [69])
for modelingartifact-centricbusinessprocesscanbefound
in [5,19]. Wealsorestrictour soundness discussion onlyon
the lifecyclebehaviorofartifactswhilediscussionsand
formal approachestodataverificationofartifact-centric
business processes(somecallartifactsystems)canbe
found inseveralexistingliteratures,e.g., [54,31,29,25,21].
4. Behavior-consistentpublicviewconstruction
In thissection,wefirstintroducethedefinitionofpublic
view anddiscussthebehaviorconsistencybetweena
createdviewanditsbase ACP-i model. Followingthat,we
presentanabstractionmethodtoconstructpublicviews
preservingthebehaviorconsistency,anddiscusshow
synchronizationdependencybetweenartifactsisaffected
by suchabstraction.Finally,weproposeatechniquefor
constructing theminimalpublicviewforagivencollabora-
tion andformalizeitintoanalgorithmofprotectingthe
information (i.e.,localprocesses)ofeveryorganizationat
the highestlevelofprivacyandautonomyduringview
construction.
4.1.Publicviewconstructionandbehaviorconsistency
Generallyspeaking,constructingapublicviewofa
particular collaborationshouldtakeintoaccountallinter-
action betweenparticipatingorganizations,particularly
the processingandexchangesofsharedartifacts.Aslife-
cycleisthemainmechanismofanartifactforspecifying
its dynamicbehaviors,andtheassociation/coordination
betweenartifactsisalsobasedonthestatesinsidelife-
cycles,wetakeitnecessarytoconstructpublicviewsbased
on lifecyclesby blinding off the privatepartwhilepreser-
ving theglobalcoordination.Weproposeourabstraction
techniquetohelporganizationsrevealonlytheirnecessary
steps thatarerequiredtocompletethecollaboration.
Shared artifactsarethemainconcernastheyareusedby
more thanoneorganization.Thisrequirementraisesthe
questionofhowtodecidewhichprocessingpartofa
shared artifactshouldbeabstractedsuchthatthe
abstractedpartdoesnotaffectthecoordination.Basedon
this requirement,weobservethatthepartofashared
artifact interactingwithlocalartifact(s)andaprocessing
step ofthesharedartifactownedbyasingleorganization
should beabstracted.Asdiscussedin Section 3.1, thisis
because suchpartisdeemedaslocalprocessingofthe
shared artifactanditshouldnotberevealedtoother
parties (outofinterestandprivacyconcern).Assuch,a
constructedpublicviewshouldhavealllocalartifactsof
every organizationhidden,andhaveallpartsofshared
artifacts thatinteractwithlocalartifactsabstracted.
Next,wediscussthe ACPabstractionmethod for con-
structing publicviewsthatderivefromanunderlying ACP-i
model. Themethodisdiscussedbasedonthefollowingtwo
points:
Abstractionofnon-synchronizedpartoflifecycle. Itiseasy
to understandthatapartofthelifecycle(calledlifecycle
fragmentorfragment)isconvertedintoeitherasingle
stateorasingletransitionduringthelifecycleabstrac-
tion. In Section 4.2, wewillintroduceageneraltechni-
queforstate/transitionabstractionthatcanbeapplied
directlytoalifecyclefragmentofindividualartifact.
Abstractionofsynchronizedpartoflifecycle. Apartfrom
the isolatedabstraction,wealsoconsiderhowmultiple
synchronizedfragments(via sync rules) ofdifferent
artifact lifecyclescanbeabstracted.Weobservethat
the abstractionofonesynchronizedendcallsforthe
abstractionofthecorrespondingendduetoconsistency
preservation.Bothabstractedfragmentsoftwolife-
cyclesmuststillsomehowbeeithercorrectlysynchro-
nized ornone.Ifanentirelifecyclesynchronizingwitha
fragmentofanotherlifecycleistobeabstracted,the
former istotallyunsynchronizedandshouldbeconsid-
ered asanembeddedfragmentoftheabstractedlife-
cycleofthelatter. Section 4.3 discusses thisissuein
more detail.
Based onan ACP-i model of inter-organizationalpro-
cesses, organizationscanconstructtheirpublicviewby
abstractingtheirsharedartifactsandtheirlocalartifacts.

Wedefineapublicviewbyapplyingthe abstractionfunc-
tion to mapacomplete ACP-i model toitspublicview.
Definition 12. (Public viewandACPabstraction).Given
ACP-imodel Π^ ¼ ðZ; V; R; L; γÞ, paΠ^ ¼ ðZp; Vp; Rp; Lp; γpÞ denotesapublicviewof Π^ , where Zp; Vp; Rp; Lp; γp are
sets ofabstractartifacts,abstractservices,abstractbusiness
rules, organizationroles,androlemappingfunctionofthe
public view,respectively. ACPabstractionfunction is defined
as pa: Zp
[ Vp
[ Rp
[ Lp
[ γp-Z [ V [ R [ L [ γ
which maps paΠ^ to Π^ . pa is atotalmappingfunctionwith
the followingconditions:
paΠ^ and Π^ haveidenticalsetsoforganizationroles,
paΠ^ contains everyabstractsharedartifact,i.e.,
8CAZ; (CiAZp; γðCÞ

41-ðpaðCiÞ 4 γpðCiÞ

41Þ
each abstractsharedartifactin paΠ^ has anidenticalrole
set toitscorrespondingconcreteartifactin Π^ , i.e.,
8CiAZp; (CAZ; paðCiÞ ¼ C - 8lAγpðCiÞ; lAγðCÞ
every ruleandtaskdefinedin Π^ must beprojectedto
some abstractruleandabstracttask,respectively,defined
in paΠ^ , i.e.,
8riAR; (rARp; paðrÞ ¼ ri 48viAV; (vAVp; paðvÞ ¼ vi
if anentirelocalartifactin Π^ is hiddenin paΠ^ then the
followingholds:
instate
rolemapping γp for abstractartifacts,tasks,andbusiness
rules holds
8CiAZp; γpðCiÞDL48viAVp; γpðviÞAL48riARp; γpðriÞAL
Example 4. Fig. 5 illustratesanexampleofanagreed
public viewthatcanbeconstructedfromthepurchasing
processintroducedin Fig. 1. Wecanseethatthepublic
view isachievedbyabstractingthreesharedartifacts PO,
SO, and IV and removingalllocalartifactsofeachorganiza-
tion. Itispossiblethat,duetoaimingtoachievehigher
level ofabstraction,abstractstatesmaybeintroducedin
the publicview,e.g., approving, supplying, unpaid are
abstractstatesin Fig. 5.
Notethelabelingofabstractstateisdonemanuallyafter
lifecycleabstraction.Participatingorganizationsshould
agree onchoosingareasonablenameofanabstractstate
in theirpublicview.Onceapublicviewisconstructed
based onitsunderlying ACP-i model, itisveryimportantto
ensure thevalidityofthepublicview.Asalreadymen-
tioned, inthisarticleweonlyfocusonthebehavior
perspectiveofACPmodels,andthuswedefinethevalidity
of publicviewsintermofthebehaviorconsistency
betweenaviewanditsbasemodel.Inourrecentwork
[96], wehaveproposedabehaviorconsistencychecking
approachcalled B-consistency tocheckwhetheraspecia-
lized processderivedfromthebaseprocessisconsistently
observable.Here,weusethe B-consistency notion tocheck
whether thebehaviorofapublicviewisconsistentwithits
underlyingmodel.
Let ℒy be thelifecycleofapublicviewconstructedby
abstractingitsbase ACP-i lifecycle ℒx. Wearetocheck
whether abstractlifecycle ℒy has consistentbehaviorswith
its baselifecycle ℒx. Intuitively,ifeachfiringsequenceof
transitionsin ℒx, disregardingstatesandtransitionsinan
abstractedL-fragment,isobservableasthesamesequence
as of ℒy, ℒy is saidtobe behavior consistent with ℒx. Our B-consistency
relationbetweentwolifecyclesisdefinedwith
the helpofbi-simulationequivalenceinprocessalgebra [9].
By abstractingalifecyclefragmentintoa silent (τ) action,
we canapplyweakbi-simulationbetweenalifecycleand
its abstractedone.
Definition 13. (B-consistent, C). Let ℒx ¼ ðSx; sinit
x ;)xÞ
and r:be twolifecyclesand Sxy ¼ Sx Sy be asetofstates
that commonlyexistin ℒx and ℒy. ℒy and ℒx aresaidto
be B-consistent (denotedas ℒyCℒx) iff,
8si; sjASxy; (ðsi; r; g; sjÞA)x; 8skASy Sxy; si)n
ysk-sk)n
ysj
8si; sjASxy; ∄ðsi; r; g; sjÞA)x; 8skASy Sxy; :ðsi)n
ysk -sk)n
ysjÞ
Notethatasdefinitionof B-consistency is generalized,it
can beusedforcheckinganytypeofalifecycle(i.e.,ACP
lifecycles,artifactlifecycles,orcompositelifecycles).
Example 5. The lifecyclein Fig. 6(a) isnot B-consistent
with the lifecycleinFigure(b),i.e., . Thisisbecause,
in somefiringsequencesoftransitionsinthelifecyclein
Fig. 6(b), state a can reachstate c(throughstate x2) without
passing state b; and,state a can reachitselfviastate x4
without passingstate b. Incontrast,wecanseethat
ℒaCℒc and ℒaCℒd in Fig. 6(c) and Fig. 6(d), respectively.
4.2. Abstractionofnon-synchronizedlifecycle
Next,weintroducenotionoflifecyclefragment(called
L-fragment) forcapturingthepartofanartifactlifecycleto
be abstractedinthepublicview.OnceanL-fragmentis
identified inalifecycle,weapplytheabstractionfunction
tomap L-fragment to aspecifiedabstractstateorabstract
transition(s)inanabstractACPmodel(i.e.,apublicview).
Definition 14. (LifecyclefragmentorL-fragment, Π^ ¼
ðZ; V; R; L; γÞ, find_Lf ). GivenACPmodel Π, L-fragment
γðCÞ of lifecycle ℒx is anonemptyconnectedsub-lifecycleof
ℒx. Itcanbedefinedas ℓℒx ¼ ðS;); )in; )out Þ where,
Purchase Order(PO)
closed delivering
confirmed
Shipping Order(SO)
In transit arrived
Invoice (IV)
cleared unpaid
billing
approving
canceled
supplying filled
issued
Fig. 5. An exampleofanagreedpublicviewbasedontheprocessin
Fig. 1.
S. Yongchareonetal./InformationSystems47(2015)5160 –81

SDℒx:S fsinitg [ Sf is anon-emptysetofstatesof ℓℒx ,
where Sf is asetof final statesof ℒx,
) DS RℒxGℒx SDℒx: ) is asetoftransitionsof ℓℒx ,
where Rℒx and Gℒx aresubsetsofbusinessrulesand
guards,respectively,definedin ℒx,
)in ¼ℒx:) ððℒx:S SÞRℒx GℒxSÞÞ is asetof entry tran-
sitions into ℓℒx ,
)out ¼ℒx:) ðS RℒxGℒx ðℒx:S SÞÞ is asetof exit transi-
tions from ℓℒx .
Wedenote ℓ!ℒc (or ℒcgℓ) if ℓ is anL-fragmentof
lifecycle ℒc of artifact C. Inaddition,wealsodefine
function f ind_Lf ðC; SÞ to returnL-fragment ℓ if ℓ consists
of asetofstates S of artifact C such that ℓ:S ¼ S and ℓ!ℒc;
otherwise,return null if suchanL-fragmentcannotbe
found.
Noticethat,givenavalidinputsetofstatesofanartifact,
thereisonlyonecasethat f ind_Lf returns null – that is
when thesetcontainsonlyan init stateand final state(s)of
that artifact.
ToensureL-fragment ℓℒx is correctlyformedbya
connectedsub-lifecycleofitsentirelifecycle ℒx, weconfine
that foreachstate s in ℓℒx :S, thereexistsasequenceof
transitionsfromanentrytransitionin )in to s and from s
to anexittransitionin )out. soundness propertycanalso
be appliedto L-fragment providingthatanyL-fragmentisa
sub-lifecycleofitsentirelifecycle.
Notethatbasedontheconditionofentryandexit
transitionsofL-fragment,anentry/exittransitionmustbe
fired from/toastateinsidetheL-fragment.However,there
is norestrictiononthenumberofentrystatesandexit
statesofL-fragment.
Next,weidentifyaspecifictypeofL-fragmentbasedon
its atomicitypropertywhichisrestrictedbymeansof
single-entry-single-exit(SESE)fragmentoflifecycle.How-
ever,weadaptittoourL-fragmentdefinitionbyallowing
the structureofmultiple-entrytransitionsandmultiple-
exittransitionsinsteadofsingleentryandsingleexitstates.
Here, wedefinesuchL-fragmentas AtomicL-fragment.
Definition 15. (AL-fragment,NAL-fragment).Given L-fragment
ℓℒx ¼ ðS;); )in; )out Þ of lifecycle ℒx, ℓℒx is
called an AL-fragment iff, allentrytransitionsin )in have
the samesourcestateandallexittransitionsin )out have
the sametargetstate.Otherwise, ℓℒx is classifiedas NAL-
fragment (non-atomicL-fragment).
Example 6. Fig. 7 showsexamplesofdifferenttypesofL-
fragments.In Fig. 7(a), L-fragments ℓ1 and ℓ2 havesingle
entry state s1 and singleexitstate s4; therefore,both ℓ1 and
ℓ2 are AL-fragments.WecanseethatL-fragments ℓ3, ℓ4,
and ℓ5 in Fig. 7(b) areNAL-fragmentsas ℓ3 has multiple
exitstates,andboth ℓ4 and ℓ5 havemultipleexitstatesand
multiple entrystates.
Based onabovenotionofL-fragment,givenacomplete
ACP-i model wecanusethesetwoabstractionmechanisms
togetherwithL-fragmentstoconstructanabstract ACP-i
model whichcanbeusedtorepresentthepublicviewofits
base model.Next,wediscussthetwooutputtypesofan
abstractionoperation: abstracttransition and abstractstate.
In mostcases,anabstractionoperationshouldyieldan
abstracttransitionasthetransitionrepresentsanatomic
and uninterruptablestepfromonestatetoanotherstatein
the lifecycle.However,insomecases,wemayseethatan
abstractstateisyieldedinstead.Forinstance,considerthe
PO artifact inthepurchasingprocessshownin Fig. 1 and
compare itwithitspublicviewin Fig. 5, wecanseethatthe
approving state inthepublicviewisanabstractstateofa
lifecyclefragmentconsistingofstates created and on_hold.
There aretwopossibleunderlyingreasonssupportingthis
case. First,anabstractstateisspecifiedinthedesignofan
organization orinthemutualagreementofthecollabora-
tion. Second,afragmentcannotbeabstractedintoasingle
abstracttransition—this isbecausethefragmentisnot
atomic(i.e., NAL-fragment). Theresultofmultipleabstract
transitionsforL-fragmentmakesitdifficulttodecideon
drawingaprojectionfromapartofthefragmenttoan
abstracttransition.Therefore,apossiblesolutionistouse
an abstractstatetoremovetheambiguityofwhatis
abstractedinsuchtransitions.Here,weshowdifferent
cases ofL-fragmentabstractionin Fig. 8.
Example 7. Fig. 8(a) and Fig. 8 (b) showtheabstractions
for abstracttransitionofL-fragmentsinartifact A1 and
artifact A2, respectively,while Fig. 8(c) showsacaseof
abstractionforabstractstateofartifact A2. Wecanseethat
both L-fragmentsin A1 and A2 are AL-fragments. However,
consider theL-fragmentofartifact A3 in Fig. 8(d) whichis
an NAL-fragment (due tomultipleexitstates s4 and s5), its
abstractiondoesnotresultinasingleabstracttransition.As
alreadydiscussed,multipleabstracttransitionsareambig-
uous. Therefore,totacklethisissue,theabstractionneeds
to resultinanabstractstateinstead,whichisshownin
Fig. 8(e). Notethatwediscussthisabstractstateindetailin
Definition 17 with anexamplein Fig. 9.
Next,wedefine lifecycleabstractionmapping function to
map anabstractelementinabstractlifecycleontoastateor
transitioninthebaselifecycle,whichisshownin Definition
a b
c
d a b
c
x d
x x
a b
c
d
x x
x
x x
x
a
c
x x d
x
l1
l2
l3
l4
Fig. 6. Examples ofabstractlifecycle(a),itsbaselifecycles(b),(c)and(d)(takenfrom [96]).

16. Thenin Definition 17, wedefinetwo abstractionfunc-
tions that areusedtoconstructanabstractlifecycle.These
functions arebasedonthepreferredoutputoftheabstrac-
tion—that isabstractstateorabstracttransition.
Definition 16. (Lifecycleabstraction(la)).Letartifactlife-
cyclele ℒ0Cx ¼ ðS0; sinit ; )0Þ in anabstractACPmodel Π0be
an abstractlifecycleofartifactlifecycle ℒCx ¼ ðS0; sinit ; )Þ
in abaseACPmodel Π. Wedefine lifecycleabstraction
mapping function laΠ0-Π
ℒ0Cx
-ℒCx
: S0[ )0 -S[ ), where
laΠ0-Π
ℒ0Cx
-ℒCx
is atotalfunctionthatmapsanabstracttransition
in )0 and anabstractstatein S0 onto astateanda
transitionin ℒCx . Wewrite la without itssuperscription
or itssubscriptionifacontextisclear.
Definition 17. (Abstractionfunctionsforabstracttransi-
tion (la_tran)andforabstractstate(la_state)).LetL-
fragment ℓCx of artifactlifecycle ℒCx ¼ ðS; sinit ; )Þ to be
abstracted.Wecanabstract ℓCx into asetof abstract
transitions and an abstractstate (if applicable)in abstract
lifecycle ℒ0Cx ¼ ðS0; sinit ; )0Þ via thetwofollowingabstrac-
tion constructionfunctions:
function la_tranðℒCx ; ℓCx Þ returns ℒ0Cx by abstracting ℓCx
into asingle abstracttransition,
function la_stateðℒCx ; ℓCx ; s0Þ returns ℒ0Cx by abstracting
ℓCx intosingle abstractstates0 and corresponding
abstracttransitionsrelatedto s0.
Functions la_tran and la_state can beexpressedby
lifecycleabstractionmappinglaℒ0Cx
-ℒCx as follows.
(a) Let ℓCx be an AL-fragment with entrystate si and exit
state sj. ℓCx can beabstractedintoabstracttransition
C1
s1
s4
s2 s3
C2
s1
s4
s2 s3
C4
s1
s4
s2
s6
s5
l1 l2 l4
C3
s1
s4 s5
s3
l3
C5
s1
s4
s2 s3
s6
s5
l5
s2 s3
Fig. 7. Examples ofL-fragmentsandNAL-fragments.
A’2
s1
s4
A2
s1
s4
s2 s3
A’’2
s1
s4
A2
s1
s4
s2 s3 sx
A’’3
s1
s4
A3
s1
s4
s2 s3 sx
s5 s5
A’1
s1
s4
A1
s1
s4
s2 s3
A’3
s1
s4
A3
s5 s5
s3
s1
s4
s2
Fig. 8. Abstractionsforabstracttransitionsandabstractstates.
A1 A’1
s1
s4
sx
s6
s5
A1
s0
s7
A1
s0
s7
OR sy
s1
s2 s3
s5
s0
s7
s4 s6
A
B
Fig. 9. An abstractiononanexpandedNAL-fragment.

si)0Sj by applyingfunction la_tran. Wehave
ℒ0Cx ¼ la_tranðℒCx ; ℓCx Þ such that,
laðsiÞ¼s
i 4 la s j ¼ sj,
8sAℓCx :S; laðsi )0 sjÞ ¼ s,
8)lAℓCx : ); laðsi )0 sjÞ¼)l.
(b)
Let ℓCx be an AL-fragment with entrystate si and exit
state sj. ℓCx can beabstractedinto abstractstates0AS0
with asetof abstracttransitions ) 0z by applying
function la_state. Wehave ℒ0Cx ¼ la_stateðℒCx ; ℓCx ; s0Þ
such that,
8sAℓCx :S; laðs0Þ ¼ s,
8)lAℓCx :) ðℓCx :)in [ ℓCx :)out Þ; laðs0Þ¼)l,
8)nAℓCx :)in; laðsi )0 s0Þ¼)n,
8)oAℓCx :)out ; laðs0 )0 sjÞ ¼)o.
(c)
Let ℓCx be an NAL-fragment with asetofentrystate Sen
and exitstate Sex. ℓCx can beabstractedinto abstract
state s0AS0 with asetof abstracttransitions ) 0z by
applyingfunction la_state. Wehave ℒ0Cx ¼ la_stateðℒCx ; ℓCx ; s0Þ such that,
8sAℓCx :S; laðs0Þ ¼ s,
8)lAℓCx :) ðℓCx :)in [ ℓCx :)out Þ; laðs0Þ¼)l,
8smAℓCx :Sen; (snAℓCx :S; sm ) s0 ) 0z-laðsm ) s0Þ ¼ sm ) sn,
8soAℓCx :Sex; (spAℓCx :S; s0 ) so ) 0z-laðs0 ) soÞ ¼ sp ) so.
It isworthmentioningthatanabstractbusinessrule,
which firesanabstracttransition,containsno defined
predicates.Ifabusinessruleinabaselifecycleisabstracted
in anabstractlifecycle,thenany defined predicateinthe
rule shouldberemovedfromtheabstractedruletoavoid
overrestrictiononartifactattributesthatmayprohibit
firing theabstracttransition.
Example 8. Fig. 8(a) and Fig. 8(b) showtheabstract
transitionsresultedfromapplyingfunction la_tran to AL-
fragments,while Fig. 8(c) showstheabstractstategener-
atedfromfunction la_tran on anAL-fragment.Ontheother
hand, Fig. 8 (e) showstheabstractstateandrelatedabstract
transitionsasanoutputofabstractionbyapplyingfunction
la_state on aNAL-fragment.
Next,wedefine B-consistent abstraction based onthe
lifecycleabstractionmapping,andthenweshow,in
Theorem 1, thatapplyingeitherfunction la_tran or func-
tion la_state togenerateanabstractlifecyclefromitsbase
lifecyclealwayspreserves B-consistency.
Definition 18. (B-consistentabstraction, Cla). Letartifact
lifecycle ℒ0Cx ¼ ðS0; sinit ; )0Þ in abstractACPmodelΠ0 be an
abstractlifecycleofartifactlifecycle ℒCx ¼ ðS; sinit ; )Þ in
ACPmodel Π based on lifecycleabstractionmapping func-tion
laΠ0-Π
ℒ0Cx
-ℒCx
. If ℒ0CxCℒCx , thenwesaythat ℒ0Cx is a B-consistent
abstraction of ℒCx , denotedas ℒ0CxClaℒCx .
Theorem1. (Non-synchronizedlifecycleb-consistent
abstraction). Let lifecycle ℒ0Cx
be anabstractlifecycleof ℒCx
by abstractingL-fragment ℓCx where ℓCx!ℒCx . Given
ℒ0Cx ¼ la_tranðℒCx ; ℓCx Þ, we have ℒ0CxClaℒCx . Correspond-
ingly, ℒ0CxClaℒCx holds for ℒ0Cx ¼ la_stateðℒCx ; ℓCx ; s0Þ where
s0Aℒ0Cx :S.
Wecanprove Theorem1 by applying B-consistency
checkingtothecomparisonbetweeninputlifecycleand
output (abstract)lifecyclebasedonthethreeusecasesof
those twoabstractionfunctions.Considerthefirsttwo
cases (a)and(b)in Definition 17. Weknowthatabstracting
an AL-fragment alwaysproducesasingleabstracttransition
or abstractstate(withsingleentrytransitionandsingleexit
transition)thatstillpreservestheatomicityofthefragment
to beabstracted.Thus,theoutputlifecycleisconsistent
with itsbase.Forthethirdcase(c)in Definition 17, we
generateasingleabstractstatewiththerestrictiononits
abstractentrytransitionsandexittransitions.Similarto
case (b),theabstractstaterepresentstheinternalbehavior
of theabstractedfragmentanditisatomic.
Please notethat,in Definition 17(c), weuseabstract
states toallowtheabstractionof NAL-fragments; however,
this abstractionhastomeetcertainconditionsforthe
abstractentryandexittransitionsoftheabstractstate.
For instance,considertheabstractionin Fig. 8(e). Entry
transition s1)sx abstractstwooriginalentrytransitionsof
its fragment(s1)s2 and s1)s3) andexittransition sx)s4
abstractstwooriginalexittransitions(s2)s4 and s3)s4).
Nevertheless,wecanseethatexittransition sx)s5 should
abstractonlyforoneexittransition s3)s5. Alternatively,if
we donotwanttohaveanabstractstateastheresultof
abstractionofNAL-fragmenttodecidetheappropriate
trigger conditionsfortransitionsduetotheaboveaddition
mechanism, thenwemayexpandtheNAL-fragmenttillit
satisfies theconditionofAL-fragment(ifpossible).This
requiresthemodelertofindapossibleAL-fragmentfrom
the expanded-boundaryofNAL-fragment.Ifsuchan
expandedfragmentcannotbefound,themodelermay
decide toimplementanabstractstatefortheabstraction.
Taketwoabstractions(A)and(B)in Fig. 9, forexamples.On
one hand,abstraction(A)on NAL-fragment consisting of
states s2 and s3 can resultinabstractstate sx and four
abstracttransitions.Ontheotherhand,withalternative
abstraction(B),theboundaryofthefragmentkeeps
expandingtillitsatisfiestheconditionofAL-fragment.
Wehavetheexpandedfragmentthatcoversallstatesand
transitionsbetweenstates s0 and s7. Then,wecanabstract
the fragmentintoeitherabstractiontransition s0)s7 or
abstractstate sy.
Next,wepresentanalgorithmtofindtheminimalAL-
fragment ofaninputL-fragment.Thealgorithmgetsan
inputfragmentandexpandsitsboundaryuntilthe
expandedfragmentsatisfiestheconditionofAL-fragment
(in Definition 15). TheoutputAL-fragmentisminimalasin
an iterationofthealgorithm,itfindsthenearestsourceand
target statesandaddsthemintothefragment(Lines8and
10).IftheinputisalreadyaqualifiedAL-fragmentthenthe
fragment itselfisreturned(Line11).Otherwise,ifthe
function cannotfindavalidAL-fragment,thenreturns null.
Algorithm1.(function find_minAL). Finding aminimal
AL-fragmentfromanL-fragment
Input: L-fragment ℓCx of artifact Cx in ACP-i model Π^ .
Output: AL-fragment ℓ0Cx if found;otherwise null is returned.
1. ℒyℓ0Cx ¼ ℓCx ;
2. repeat
3. Sen
¼a setof entry states of ℓ0Cx ;
4. Sex
¼a setof exit states of ℓ0Cx ;
5. if (jSen
j 41 or jSex
j 41)
6. then
7. if jSen
j 41 then

8. ℓ0Cx includes allstatesin Sen and theirrelated exit transitions;
9. if jSex
j 41 then
10. ℓ0Cx includes allstatesin Sex and theirrelated entry
transitions;
11. else if (jSen
j ¼ 1 and jSex
j ¼ 1) then return ℓ0Cx ;
12. until Sen
¼ ∅ and Sex
¼ ∅
13.return null;
Based on Theorem 1 along withthehelpof f ind_minAL
function forNAL-fragmentabstraction,wecanconstructa
consistentpublicviewofanindividualartifactlifecycleby
abstractingitsnon-synchronizedpartofthelifecycle.Next,
we discusshowafragmentofalifecyclethatsynchronizes
with afragmentofanotherlifecyclecanbeconsistently
abstracted.
4.3. AbstractionofsynchronizedL-fragments
In thissection,wediscusshowthesynchronization(via
sync rules) betweentwolifecyclescanbeabstractedin
detail. Technically,weneedtoanswerthefollowing
questions.
What istheresultofabstractinganL-fragment(ora
whole) ofonelifecyclesynchronizedwithanL-fragment
of anotherlifecycle?
What istheconditionthatmakesanabstractsynchro-
nization consistentwithitsoriginalsynchronization?
Here, weusethesameL-fragmentabstractionmethod
to abstractthesynchronizedpartswiththeconsideration
of synchronizationstructureandbehavior.However,in
order tocapturesynchronizationdependenciesbetween
lifecycles,weneedtoextendthedefinitionofL-fragment
for asynchronizedregion(called S-region) whichrepre-
sents synchronizedL-fragmentsbetweenlifecycles(called
SL-fragments). Withatargetfragmentofanartifactandthe
sync rulesusedwithinthefragment,wecanidentifya
counter-synchronizedpart(s)oftheotherartifact(s)thatit
interactswith.
Definition 19. (Sync ruleforsynchronizedL-fragments, φ).
GivenACPmodel Π, asetofsyncrulesthatisusedwithin
two synchronizedL-fragments ℓx and ℓy can bedefinedas
follow:
φðℓx; ℓyÞ ¼fr
AΠ:Rj (ðsi; r; g; sjÞA ℓx:
) 4(ðsm; r; g; snÞAℓy: )g
It isnotedthatasyncruleistransitive,i.e.,
(rAφðℓx; ℓyÞ φðℓy; ℓzÞrAφðℓx; ℓzÞ.
Definition 20. (SL-fragmentandS-region).GivenACP
model Π, wedenote ω¼ ðΓ; Rsync) fora synchronization
region (S-region) where,
a setofsynchronizedL-fragments Γ¼ fℓC1 ; ℓC2 ; …;
ℓCx g, ℓCi AΓð1rirxÞ is asynchronizedL-fragment,
called as SL-fragment, of artifactlifecycle ℒCi ðCiAΠ:ZÞ,
!RsyncDΠ:R is asetof sync rules that isusedto
synchronizetransitionsbetweenL-fragmentsin Γ such
that,
8rAΠ:R; (ℓCi ; ℓCj AΓ; 8rAφðℓCi ; ℓCj Þ; rARsync
Example 9. In Fig. 10(a), wehaveS-region ωa with SL-
fragments l1 of artifact A1 synchronizedwith SL-fragmentl2
of artifact A2 via syncrules r1 and r2. In Fig. 10 (b), S-region
ωb has two SL-fragmentsl3 and l4 with syncrules
Rsync
¼ fr1; r2; r3g. Noticethatsyncrule r4 is excludedfrom
ωb as itisnotusedforthesynchronizationbetween l3 and
l4.
Next,westudytheatomicitypropertyofS-regionby
determiningthecomposabilityofcontainedSL-fragments
and theboundnessoftheirsynchronizationbehavior.
4.3.1.AtomicityofS-region
Here, weproposeafragmentalcompositiontechnique
tochecktheatomicityofS-region.Firstweseethatthe
composition betweentwosynchronizedL-fragments
resultsinacompositeL-fragment.Thenwecanapply
atomicitycheckingtothecompositeL-fragment.Assuch,
we needtoobservetheconditionsforSL-fragmentsthat
make thecompositeL-fragmentatomic.Now,wedefine
compositeS-region based on lifecyclecomposition (in
Definition 9).
Definition 21. (CompositeS-region).GivenACPmodel Π,
let S-region ω¼ ðfℓCx ; ℓCy g; Rsync) ofL-fragment ℓCx of artifact
CxAΠ:Z and L-fragment ℓCy of artifact CyAΠ:Z where ℓCx
and ℓCy aresynchronizedviabusinessrules RsyncRsync. The
compositeS-region of ω, ω¼ ℓCx ℓCy , istuple ðS;);
)in;)out Þ where eachsetelementin ω has thesame
definition correspondingtotheelementofL-fragment,i.e.,
inω can beconsideredasanL-fragment(orSL-fragment
if thecompositefragmentstillhassomesynchronizationto
otherfragmentofdifferentartifact).
It isnotedthata compositeS-region is consideredasa
sub-lifecycleofthecompositionbetweentwoentirelife-
cycles.Tohavea(minimalandsufficient)completeviewof
the compositionwedrawadashedarrowforatransition
betweenacompositestateexcludedfromtheS-regionand
a compositestatethatisanentryorexitstateoftheS-
region,asexemplifiedin Fig. 11. Fig. 11 (a) and(b)showthe
resultsofSL-fragmentcomposition, compositeS-regions
ωa and ωb, forS-regions ωa and ωb in Fig. 10 (a) and
in Fig. 10 (b), respectively.
Example 10. In Fig. 11, ωa has compositestate(s2; s5),
and (s4; s7) asitsentrystateandexitstate,respectively.
Likewise, ωb has twoentrystates(s2; s5) and(s9; s6), and
twoexitstates(s4; s7) and(s4; s8). Notethatcomposite
state(s1; s5) isoutofscopeof ωa and ωb, soitisexcluded
from ωa and ωb, respectively.
Next,wevalidateatomicitypropertyof S-region by
checkingwhetherSL-fragmentsoftheS-regioncanbe
composed intoanatomiccompositeS-region.Weconsider
the propertyof AL-fragment to define atomicS-region (AS-region),
i.e., AS-region must haveallentrytransitionfired
fromthesame(composite)sourcestateandallexittransi-
tions firedtothesame(composite)targetstate.

Definition 22. (AS-regionandASL-fragment).GivenACP
model Π, let S-region ω¼ ðΓ; Rsync) and ZΓDΠ:Z be asetof
artifacts whereofwhichhasitsL-fragmentdefinedin Γ.
The compositionofallSL-fragmentsin Γ satisfies the
propertyof AL-fragment iff, forevery ℓCi AΓ,
ℓCi is an AL-fragment,
8ℓCx ; ℓCy AΓ; 8rAφðℒCx ;ℒCy Þ; (ssAℓCi :S; ss)rsAℒCi :
)-ss) r
sAℓCi : ) 4rARsync
8ℓCx ; ℓCy AΓ; 8rAφðℒCx ;ℒCy Þ; (stAℓCi :S; s)rstAℒCi :
)-s) r
stAℓCi : ) 4rARsync
8ℒCj ðCjAΠ:Z ZΓ
Þ;φðℓCi ;ℒCjÞ ¼ ∅.
By holdingaboveconditions, ω can beconsideredasan
AS-region. WealsocalleachL-fragmentin Γ as ASL-
fragment of ω.
Notethattheconditionsin Definition 22 are usedto
restricttwoSL-fragments(tobecomposedforS-region)to
include everytransitionandcorrespondingsyncrulethat
areusedforonlythesynchronizationbetweenL-fragments
in Γ. IfanS-regioncontainsmorethantwoSL-fragments,
then, likelifecyclecompositionforACPmodel,wecan
check theAS-regionbyperformingiterativecomposition
for eachSL-fragmentinthatS-region.Itisalsoworth
mentioning thatthecompositionofSL-fragmentsforAS-
region holdsassamecharacteristicsasforthelifecycle
composition – that iscommutativeandassociative,i.e.,
ℓCx ℓCy ¼ ℓCy ℓCx and ℓCx ℓCy ℓCz ¼ ℓCx ðℓCy
ℓCzÞ ¼ðℓCx ℓCyÞ ℓCz .
Example 11. In Fig. 10 (a), ωa is anAS-regionasboth
L-fragments l1 and l2 areAL-fragmentswithallrelatedsync
rules (r1 and r2) residingwithinthem.Assuch,the
resultingfragmentfromthecompositionbetween l1 and
l2 is thenatomic,asshownin Fig. 11 (a). Incontrast,in
Fig. 10 (b), wecanseethatL-fragment l4 cannotsatisfythe
propertyofAL-fragment,andL-fragment l3 does not
include transition s5)r4 s6 wheresyncrule r4 exitsinentry
transition s5)r4 s6 of l4. Therefore, ωb cannotbeconsidered
as AS-region.
Example 12. Now,weillustratethecasethatanS-region
contains morethantwoSL-fragmentswhereoneofwhich
synchronizedonthe(nested)sub-fragmentofSL-fragment,
as shownin Fig. 12. AssumeS-region ω1 for SL-fragments
{l1; l2; l3}, ω1 cannotbeconsideredasanAS-regionas l1 has
some syncrulesthatareusedforthesynchronization
betweenitssubL-fragment l5 and L-fragment l4 of the
lifecycleofartifact A4. Therefore,weneedtoinclude l1 into
the S-regioninordertosatisfythepropertyofAS-region.
In thenextsection,wediscussabouthow AS-region can
be usedfortheabstractionofsynchronization.
A1 A2
s1
s2 s4
s3 s5 s7
r1
s6
r2
l1 A1 A2
s1
s2 s4
s3 s5 s7
r1
s6
r2
s9
s8
l2
l3
l4
a b
r4
r3
ω ω
Fig. 10. An exampleofS-regionsandSL-fragments.
Fig. 11. Composite S-regionsofSL-fragmentsbasedon Fig. 10.
A1
s1
A3 A2
A4
s2
s1
s3
s2
s1 s2 s4 s3
l4
s3 s5
s4
s6
l1
s2
s3
s1
l2
l3 l5
Fig. 12. An S-regionwithsubSL-fragments.

4.3.2. SL-fragmentabstraction
Here, wedefinetheabstractionrelationofthesynchro-
nization betweentwoabstractartifactsintheabstractACP
model andthesynchronizationbetweentwoartifactsinits
base ACPmodel.
Definition 23. (Synchronization(Sync)abstraction).Let
artifact lifecycles ℒ0Cx and ℒ0Cy in ACPmodel Π0 abstract
artifact lifecycles ℒ0Cx and ℒ0Cy in baseACPmodel Π with
lifecycleabstractionmappings laℒ0Cx
-ℒCx and laℒ0Cy-ℒCy ,
respectively.Wecandefine sync abstractionmapping func-tion
saΠ0- Π
ðℒ0Cx ;ℒ0Cy ÞðℒCx ;ℒCy Þ
:φðℒ0Cx ;ℒ0Cy ÞφðℒCx ;ℒCy Þ that isused
to projectthe abstractsyncrule for ℒ0Cx and ℒ0Cy onto its
base syncrulefor ℒ0Cx and ℒ0Cy .
Notethat saΠ0 - Π
ðℒ0Cx ;ℒ0Cy Þ ðℒCx ;ℒCy Þ
is atotalfunctionandwe
may write sa without itssuperscriptionandsubscriptionin
a clearcontext.
Now,wewanttoperformanabstractiononanL-
fragment thatsynchronizeswithotherL-fragment(s).Simi-
lar toabstractionfunctionfornon-synchronizedlifecycle,
we define sync abstractionfunction for abstracting AS-region
that containssynchronizedL-fragments.
Definition 24. (Sync abstractionfunction(sa_f)).Given
ACPmodel Π, letAS-region ω¼ ðΓ; Rsync
Þ to beabstractedin
abstractACPmodel Π0, where Γ ¼ fℓC1 ; ℓC2 ; …; ℓCx g and
ℓCi ð1rirxÞAΓ is anL-fragmentoflifecycle ℒCi in Π. We
define syncabstraction function sa_f ðΠ;ωÞ to return Π0
with asetof abstractartifactlifecycles L ¼ fℒ0C1 ;ℒ0C2 ; ::;ℒ0Cx g
and an abstractsyncruler0, where ℒ0Ci ð1rirxÞAL is a
lifecycleofartifact CiAΠ0:Z such that,
for every ℓCi AΓ, ℓCi is abstractedinto abstracttransi-
tions in ℒ0Ci , i.e.,
ℒ0Ci ¼ la_tranðℒCi ; ℓCi Þ;
for everysyncrule rAΠ:R that isusedtosynchronize
betweenanytwoL-fragmentsin Γ, r is abstractedinto
r0AΠ0:R, i.e.,
8ℓCx ; ℓCy AΓ; 8rAφðℓCx ; ℓCy Þ; (!r0Aφðℒ0Cx ;ℒ0Cy Þ;
sa
ðℒ0Cx ;ℒ0Cy Þ ðℒCx ;ℒCy Þðr0Þ ¼ r
Abstractsyncrule r0 that isusedtosynchronizeall
abstracttransitionstogethercanbedefinedasfollow.For
everyL-fragment ℓCi ¼ ðS; );)in;)out ÞAΓ, wehave,
(ss; stAℒCi :S S;ðss)in) n
)outst Þ
ssApre_sðr0; CiÞ4stApost_sðr0; CiÞ
Example 13. In Fig. 13 (a), wecanseethatAS-region ωa
contains twofragments l1 and l2 with syncrules r1 and r2.
When applying sa_f ðΠ;ωa), wehaveabstractlifecycleof
ℒA1 and abstractlifecycleof ℒA2 with abstractsyncrule r0.
In addition, Fig. 13 (b) showsacaseofsyncabstractionfor
AS-region ωb which containsmultipleentrytransitions
and multipleexittransitionsASL-fragments(bothASL-
fragments l3 and l4).
In theaboveexample,wedemonstratethesyncabstrac-
tion oftwosynchronizedfragments.However,itispossible
that anAS-regioncontainsmorethantwoASL-fragments.
Forwiderunderstandingofsyncabstraction,weillustratea
sync abstractionofmorethantwoSL-fragmentsin Fig. 14
(with artifact A3 extendedtotheexamplein Fig. 13 (b)).
Example 14. In Fig. 14, wecanseethatAS-region ωb
contains synchronizedfragments l3 and l4 of artifact A1 and
A2, respectively,and l5 of artifact l4. Asallthreefragments
can beconsideredasASL-fragmentsin ωb, wecanvalidly
apply function sa_f ðΠ;ωb) andtheabstractlifecyclesof
artifacts fA01; A02; A03g with abstractsyncrules fr0; r″g are
returned.
A1 A2
s1
s2 s4
s3 s5 s7
r1
s6
r2
l1
l2
a A’1 A’2
s1
s2 s4
s5
s7
r'
A1 A2
s2 s4
s3 s5 s7
r1
s6
r2
s9
s8
l3
l4
b r4
r3
s1
A’1 A’2
s2 s4
s5
s8
r'
s1
ω
ω
Fig. 13. Examples ofsyncabstraction.

Next,wediscussthecaseofanAS-regioncontainingSL-
fragmentswithanested(sub)SL-fragmentthatsynchro-
nizes withotherlifecycle.Intuitively,thesubSL-fragment
and itssynchronizedlifecycleshouldbealsotakeninto
account whenitssuperfragmenthastobeabstracted.
Therefore,weneedtoinducetheabstractiontoitssub
fragmenttogetherwithitscounterpartiftheybothcan
satisfy thepropertyofAS-region(whichisconsideredasa
sub AS-regionofthewhole).Inotherwords,wecansay
that theentireAS-regionshouldcontainsuchcounterpart
in ordertohaveavalidabstraction.Weshowanexampleof
AS-regionconsistingofsubSL-fragmentin Fig. 15.
Example 15. In Fig. 14, wecanseethatL-fragment l4 is a
synchronizedfragmentofL-fragment l5 which isnested
under L-fragment l1. Theabstractionyieldsabstracttransi-
tions withabstractsyncrule r0z- thatis s1)r0z s3 in the
lifecycleof A04 and s1)r0z s6 in thelifecycleof A01.
Next,weconsiderthecasethatthesyncabstraction
performs onanL-fragmentofoneartifactthatsynchronizes
with theentirelifecycleofoneanotherartifact.Suchwhole
lifecyclecanbeconsideredasfully-embeddedexternal
lifecycleintheL-fragment.Wesaythatlifecycle ℒCj can
be fully-embeddedinlifecycle ℒCi if thereexists
L-fragment ℓCi!ℒCi that completelysynchronizesthe
entire lifecycle ℒCj , i.e.,theentrystateandtheexitstate
(s) of ℓCj are the init state andallthe final state(s)of ℒCj ,
respectively.Itcanbeunderstoodthattheabstractlifecycle
of artifact Cj containing onlyabstracttransition(s)firing
from its init statetoits final state(s) impliesasinglestep
lifecycleandtheredoesnotexistsanyL-fragmentwithinit,
i.e., f ind_Lf ðCj; Cj:SÞ ¼ null. Thebenefitofintroducingthis
type oflifecycleabstractionisdiscussedlaterwhentaking
into accounttheconstructionofpublicview.Itisnotedthat
a lifecycleofoneartifactcanbeconsideredasfully-
embedded externallifecycleofothermultiplelifecycles.
Example 16. In Fig. 16 (a), L-fragment l1 synchronizeswith
L-fragment l2 which representsthewholelifecycleof
artifact A2. Therefore,wehave ℒA2 as anfully-embedded
lifecycleof ℒA1 . Similarly,in Fig. 16 (b), wehave ℒA3 as a
fully-embeddedlifecycleofboth ℒA1and ℒA2 .
Next,weshowthat sync abstractionfunctionsa_f pre-serves
B-consistency of betweentwosynchronizedlife-
cyclesoftheinputandtwooutputtedabstractlifecycles.
Theorem2. (synchronizedfragmentsb-consistentabstrac-
tion). Let ω¼ ðΓ; Rsync
Þ be anAS-regioninACPmodel Π that
is tobeabstracted in ACPmodel Π0 and let L be asetof
A3 A1 A2
s10
s11 s2 s4
s3 s5 s7
r1
s6
r2
s9
s8
l3 l4
b
r4
s1
r8
r r3 7
s13
s14
r6
A’1 A’2
s2 s4
s5
s8
r'
s1
s12
r5 l5
A’3
s10
s11 s14
r'’
r8
ω
Fig. 14. An exampleofanabstractionoftwoormoreASL-fragments.
A1
s1
A3 A2
A4
A’1
s1 s6
A’3
s1
s3 s4
s2
s1
s3
s2
s1 s2 s4 s3
l4
A’4
s1 s3
r'z
s3 s5
s4
s6
l1
s2
s3
s1
l2
l3
A’2
s1
s3
r'x r'y
l5
Fig. 15. An exampleofanabstractiononnestedsub-SL-fragments(cf. Fig. 12).

abstractartifactlifecyclesresultedfromapplyingsync
abstractionfunctionsa_f ðΠ;ωÞ. Then thefollowingstatement
holds.
8ℒCi ;ℒCj Afℒjℓ!ℒ4ℓAΓg; (ℒ0Ci ;ℒ0Cj AL;
ℒ0CiClaℒCi
4ℒ0CjClaℒj-ℒ0Ci ℒ0CjCℒCi ℒCi
Wecanprove Theorem 2 by using Definition 21 and
Definition 22for the B-consistency checkingbetweentwo
abstractlifecyclesandtheirbaselifecycles,andbetween
the compositionbetweentheformerandthecomposition
betweenthelatter.From Definition 24, syncabstraction
sa_f alwaysreturnsasingleabstracttransitionineach
abstractlifecycleandasinglesyncrulebetweentwo
abstracttransitions,sothecompositionofsuchabstract
transitionsalwaysyieldsanatomiccompositefragment.
The compositionofASL-fragmentsintheirbaselifecycleis
atomic andcanentirelyberepresentedbythecomposition
of abstracttransitions.
4.3.3. FindingminimalAS-region
Next,wediscusssimilarrequirementsfortheneedof
NAL-fragmentexpansion(toAL-fragment).GivenanL-
fragment ofoneartifactlifecyclethatsynchronizeswith
otherartifactlifecycle(s),wecanfindtheminimalAS-
region (whichcontainsthatL-fragment)anditsminimal
counterpart(s)inwhichtheycanbeusedasinputsfor sync
abstractionfunctionsa_f . Here,weproposetwoalgorithms
to findtheminimalAS-regionofanL-fragment.Notethat
the synchronizedcounterpartscanbemanyastheL-
fragment cansynchronizewithmultiplelifecycles.Two
proposed algorithms f ind_minASR and f ind_SR areusedto
expandtheboundaryofanL-fragmentalongwithits
synchronizedcounterpart(s)untilallsatisfythecondition
of AS-regionandASL-fragment(in Definition 22). IfnoAS-
region canbeconstructedoranL-fragmenthasnosyn-
chronizedcounterpartofanyotherlifecycle,thenthe null
valueisreturned.
Algorithm2.(function find_minASR). Finding aminimal
AS-regionfromanL-fragment
Input: L-fragment ℓCx in ACP model Π.
Output: AS-region ω¼ ðΓ; Rsync
Þ if found;otherwise null is
returned.
1. ω’ðfℓCx g; ∅);
2. ω¼ find_SRðωÞ;
3. return ω;
Algorithm3.(function find_SR). Finding anexpanded
S-regionfromaninputtedS-region
Input: S-region ω¼ ðΓ; Rsync
Þ in ACPmodel Π.
Output: ExpandedS-regionof ω or null if anySL-fragmentin ω
cannot satisfythepropertyofAL-fragment.
1. for each ℓiAω:Γ do
2. L-fragment ℓ0i ¼ find_minALðℓi);
3. if (ℓ0i ¼ nullÞ then return null;
4. else
5. ω:Γ ¼ ω:Γ [ fℓ0ig fℓig;
6. end if
7. for each ℒjAfℒCj j CjAΠ^ :Zg do
8. states Sj ¼ ∅;
9. for each rkAφðℓ0i ;ℒjÞ do
10. Sj’pre_sðrk; CjÞ [ post_sðrk; CjÞ;
11. if (∄rkAω:Rsync
Þ then rkAω:Rsync’rk;
12.endfor
13. L-fragment ℓj ¼ f ind_Lf ðCj ; SjÞ;
14. L-fragment ℓ0j ¼ find_minALðℓj);
15. if(ℓ0janullÞ
16. then
17. if ð∄ℓ0jAω:ΓÞ
18. then
19. ω:Γ ¼ ω:Γ [ fℓ0jg;
20. ω¼find_SRðω Þ;
21. return ω;
22. end if
23. else return null;
24. end if
25. end for
26. end for
Here, weusearunningexampleillustratedin Fig. 17 to
explainthealgorithmsoffunctions f ind_minASR and
f ind_SR.
Webeginwith Fig. 17 (a) byapplying f ind_minASRðl1Þ in
this example.FirstittakesL-fragment l1 of artifact A2 as an
inputandinitializesanS-regionfrom l1 and anemptysetof
sync rule.ThenitfindsthepossiblecorrespondingS-region
for l1 (bycalling f ind_SR function). Function f ind_SR starts
checkingwhether l1 can satisfythepropertyofAL-
fragment(Line3).Ifso,thenitcontinuessearchingforall
sync rulesandtheirrelatedsynchronizedstatesthatare
used tosynchronize l1 with anyotherlifecycletransitions;
otherwise,itimmediatelyreturns null. Intheiterationof
finding synchronizedpartofotherartifact,ifasetof
synchronizedstatesisfound(Lines9–12),thenafragment
consisting ofsuchsetisconstructedbycalling find_Lf
function (definedin Definition 14) – that isL-fragment l2
of artifact A1 shown in Fig. 17 (b). Next, l2 is tobechecked
whether itisqualifiedasAL-fragment.Ifitsatisfies,thenit
is addedintotheS-region(Lines13-21);otherwise,ithas
tobeexpandeduntilitcansatisfyAL-fragment.Once
qualified,itisaddedintotheS-region(Line19).After l2 is
added totheS-region,werecursivelycallfunction f ind_SR
again withtheexpandedS-regionasaninput(Line20).
Fig. 17 (c) showsAL-fragment l02 that isexpandedfrom l2.
Wecanseethat l02 introducesnewsyncrules fr5; r6g that
arenotincludedintheS-region.Therecursionwillcon-
tinue untilalltheSL-fragmentsintheS-regionareAL-
fragmentsandincludeallthepossiblesyncrulesthatare
used intheS-region.Consequently, l1 is requiredtoexpand
itself andbecomesnewAL-fragment l01, asshownin Fig. 17
(d). Afterthat,wecanseenewsyncrules fr7; r8g appear in
l01. TheS-regionneedsanotherexpansionagaintocover
those syncrules – that isL-fragment l3 of artifact A3. The
exitconditionoftherecursioniswhenthefragmentisnull
(Line 15withtheexitonLine23).Thefinaloutputofthe
f ind_SR function isanS-regionthatallthesyncrulesare
discoveredandthatcontainsonlyAL-fragments.Finally,by
completing theiterationandrecursionwithallthecondi-
tions ofAS-regionsatisfied,thefunctionreturnsthemini-
mal AS-regionconsistingofASL-fragments fl01; l02; l3g as the
output fromtheprovidedinputL-fragment l1. IftheAS-
regioncannotbeconstructedthenthefunctionreturns

A1 A2
sa
s1 s3
sa
s1
r1
s2
s6
s5
s4
s6
r4 s5
s2
r3
r2
l1
s3 r5
A1 A2
sa
s1 s3
s2
s6
s5
s4
sa
s1
s6
s5
s2
r1
r4
r3
r2
s4
r6
s3 r5
s4
r6
l'2 l1
A1 A2
sa
s1 s3
s2
s6
s5
s4
sa
s1
s6
s5
s2
r1
r4
r3
r2
s3 r5
s4
r6
l'2
A1 A2
sa
s1 s3
sa
s1
l2 r1
s2
s6
s5
s4
s6
r4 s5
s2
r3
r2
l1
s3 r5
s4
r6
A3
s1
s2
s3
r7
r8
A3
s1
s2
s3
r7
r8
A3
s1
s2
s3
r7
r8
A3
s1
s2
s3
r7
r8
l'1
A1 A2
sa
s1 s3
s2
s6
s5
s4
sa
s1
s6
s5
s2
r1
r4
r3
r2
s3 r5
s4
r6
l'2
A3 l'1
s1
s2
s3
r7
r8
l3
Fig. 17. A runningexampleforthe f ind_minASR function.
A1 A3 A2
s1
sf s4
A’2
s1
s3
s4
A’1
s1
s4
A2
A’1
s1
s3
A1
s1
s3
s2
s1
s4
s2 s3
s1
s3
s2
l1
l1 l2
sf
A2
sf
r'
s1
s2
r2
r1
l2
A’3
sf
Fig. 16. An exampleoffully-embeddedexternallifecycles.

false. WecansaytheresultedAS-regionisminimalasthe
function usethe f ind_minAL function toguaranteethe
minimal AL-fragmentexpansionintheAS-region.
Based on Theorem 2 and theuseofthe f ind_minASR and
f ind_SR functions, wecanconstructaconsistentpublic
view ofsynchronizedlifecyclesbyabstractingtheirsyn-
chronizedpartsofthelifecycles.
4.4. Consistentpublicviewconstruction
Now,weuse Theorems1and2 to formulatethe B-consistency
for theentireartifact-centricinter-organiza-
tional businessprocess.
Theorem3. (b-consistent publicview). Let paΠ^ be apublic
view of ACP-imodel Π^ constructed byapplyingsyncabstrac-
tion functionsa_f and lifecycleabstractionfunctions la_tran
and sa_state. Then paΠ^ is aB-consistentabstraction of Π^ , i.e.,
ℒpa ^ ΠClaℒΠ^ .
Theorem 3isderivedfrom Theorems1and2.
Recallthatinthepublicview,alllocalartifactsshouldbe
invisible.Onlyabstractsharedartifactsarerevealedforthe
collaboration.Inordertohidethoselocalartifactsofeach
party,thepartymustensurethatifalocalartifactsynchro-
nizes withafragmentofasharedartifact,thenthis
fragment mustbehiddenaswell.Thishidingproperty
refers totheabstractionofsuchfragment.However,ifthe
entire lifecycleofalocalartifactisabstracted,thenitcanbe
validlyhiddeninthepublicview.In Section 4.3.2, we
discuss thefully-embeddingpropertytocapturethiskind
of lifecycle.Inotherwords,ifthelifecycleofalocalartifact
is afully-embeddedexternallifecycleofthesharedartifact,
then thelocalartifactcanbehidden.Assuch,thecorre-
sponding fragment(s)inthesharedartifact(s)isalso
abstracted(byusingsyncabstractionfunction sa_f ). How-
ever,thereisacaseifthatfragmentisnotanAL-fragment,
then the sa_f function cannotbeappliedduetothe
requirementoftheinputthatmustbeAS-region(consist-
ing ofASL-fragmentsofsharedartifact(s)andlocalartifact).
Tocopewiththisissue,thenweproposetouselifecycle
abstractionfunction la_state to abstractitintoanabstract
state. Thenthelocalartifactthatsynchronizeswiththat
fragment canbeabstracted.Althoughwecanabstractan
NAL-fragmentintoanabstractstate,itishardtodecide
whether thatabstractionisvalidandconsistentintermsof
synchronizationbehavior.Thelocalartifactthatsynchro-
nizes withanypartofsuchNAL-fragmentmustbeexclu-
sivelyencapsulatedintheabstractstate.Inaddition,the
abstractstateitselfisnotconsideredasatomicifithas
multiple entryandmultipleexittransitionsfrom/todiffer-
ent states.Therefore,weallowhavingsyncabstractionfor
the abstractstateforthecasethatthewholelifecycleofthe
local artifactissynchronizedwithintheNAL-fragment.As
previouslydiscussed,representinganNAL-fragmentinan
abstracttransitionisdeemedinconsistent.
Example 17. Revisitourpurchasingprocessexamplein
Fig. 1. Wecanconstructafragmentforthe PO artifact that
consists ofstates fcreated; on_holdg. Thefragmentiscon-
sideredasNAL-fragment(duetotwoexitstates).Wecan
see thatitsynchronizeswiththeentirelifecycleofthe
Quote artifact, therefore,theabstractionofthisfragment
must yieldanabstractstatewhichrequiresthewhole
lifecycleof Quote tobeabstracted,i.e.,fully-embedded –
that isthe approving stateofabstract PO in thepublicview
shownin Fig. 5. Similarly,theentirelifecycleof PL artifact
can beabstractedandfully-embeddedinthe supplying
stateoftheabstract PO in thepublicview.
Next,weproposeanalgorithm(forafunctionnamed
f ind_minPV) tohelporganizationstoautomaticallyfindthe
minimal, consistentpublicviewfromtheir ACP-i model.
Due totheinconsistencyissueonNAL-fragmentabstrac-
tion, wedonottakeNAL-fragmentsintoaccountinthis
algorithm.Afterpresentingthealgorithm,wethenshow
howitcanguaranteethe B-consistency.
Algorithm4.(function find_minPV). Finding themini-
mal, consistentpublicviewofan ACP-imodel
Input: ACP-i model Π^ ¼ ðZ; V; R; L; γÞ.
Output: theminimalpublicviewof Π^ .
1. public ACP-imodel Π^ 0 ¼ Π^ ;
2. for each CiAfCAΠ^ 0Z jγðCÞj ¼ 1g do
3. L-fragment ℓi ¼ f ind_Lf ðCi ; Ci :SÞ;
4. AS-region ω¼ find_minASRðℓiÞ;
5. i f(ω anull)
6. then
7. Π^ 0:¼ sa_f ð Π^ 0; ωÞ;
8. artifacts Zl’Ci;
9. for each CjAfCAΠ^ 0:Z jγðCÞj ¼ 1g do
10. L-fragment ℓj ¼ f ind_Lf ðCj ; Cj :SÞ;
11. if ðℓj ¼ nullÞ then Zl’Cj ;
12. end for
13. remove all artifactsin Zl and theirrelatedabstractsyncrules
from Π^ 0;
14. Zl
¼ ∅;
15.endif
16.endfor
17. return Π^ 0;
Now,weexplainthealgorithmforthe f ind_minPV
function. First,itinitializesapublicviewasidenticalto
an input ACP-imodel. Then,itsearchesforalllocalartifacts
in thepublicview(Line2).Foreachlocalartifactfound,it
attemptstoconstructanAS-regionthatconsistsofsuch
artifact (Lines3–4). IfitisabletoconstructtheAS-region
(Line 5),thenabstractionfunction sa_f is appliedonthe
regionandtheartifactisaddedtotheset Zl and allartifacts
in Zl will belaterremovedfromthepublicview(Lines7–8).
As sa_f finds allcorrespondingASL-fragments(ifconstruc-
tible) thatsynchronizedwiththelocalartifactintoaccount
for theabstraction,thealgorithmalsosearchesforother
local artifactthatqualifiesasfully-embeddedexternallife-
cycletobeincludedin Zl (Lines 9–12).Thiswilleliminate
an unnecessarylocalartifactinthepublicview;therefore,
the numberofiterationsforfindinglocalartifactsis
reducedinthemainloop.
Fromthealgorithmwewillgettheminimal, B-consistent
public viewofthe ACP-i model. However,itdoesnot
guaranteethatalllocalartifactsareabstracted.This
depends onwhetherthelifecycleofsuchartifactscanbe

fully-embeddedaswellasthesynchronizedpartofthe
sharedartifactisanASL-fragment.Inotherwords,ifthe
fragmentisanNAL-fragment,then,aspreviouslydiscussed,
the abstractionofthoselocalartifactsmustbeachieved
manually – by abstractingeachofsuchfragmentsintoan
abstractstateinstead.Thisprocessrequiresapredefined
abstractstateforanabstractsharedartifact.
Next,weshowin Theorem 4 that our f ind_minPV
function producesaminimal, B-consistent public view.
Theorem4. f ind_minPVðΠ^ Þ returns aminimal, B-consistent
public viewof Π^ .
Wecanprove Theorem4 as follows.First,weprovethat
f ind_minPVð Π^ Þ returns acorrectpublicviewof Π^ . Thiscan
be donebyinductionoverallmappingconditionsin
Definition 12. Notethatremovinglocalartifactfromthe
public viewwhereitsentirelifecyclecanbeabstractedalso
conforms tothedefinitionofpublicview.Second,weprove
that given ACP-i model Π^ , f ind_minPVð Π^ Þ is guaranteedto
returnminimalpublicviewof Π^ . Asweusefunction
find_minASR to searchfortheminimalAS-regionthatcan
be usedasaninputoftheabstractionfunction sa_f , then
this statementisnaturallysatisfied.Last,weprovethe B-consistency
of thegeneratedpublicview.Basedon Theorem
3 and Definition 24, thepublicviewpreserves B-consistency
as function sa_f alwaysyieldsa B-consistent abstractACP
model oftheinputtedACPmodel.
Wenowconclude Section4. Insummary,thissectionhas
discussedthepublicviewconstructionmethodologyand
behaviorconsistencyandformulatesseveralfunctionsand
theoremsthatcanbeusedtoconstructthe B-consistent public
viewofthecollaboration.Italsopresentsouralgorithmsthat
helporganizationsautomaticallygeneratetheminimal
abstractpublicviewwiththeassuranceofthe B-consistency.
5. Consistentprocesschangesandprivateviews
In thissection,weproposeamechanismthatallowsa
party inthecollaborationtochangetheirlocal(private)
processwithoutaffectingthecorrectnessandconsistency
of theoverallprocess.
5.1.Localprocesschanges
Organizations mayneedtochangetheirlocalprocesses
due totheirnew(orupdated)setofbusinessrequirements
or regulationsthattheyhavetofollow.Weobservethatin
artifact-centric processes,changestolocalprocessescanbe
classified intothreetypesbasedonthethreecomponents
of the ACPmodel.
Changes toartifacts. Anorganizationmaymodify/delete/
add anattributeorastateofitslocalartifact,whichcan
be seenasstructuralchangestothedatamodelofan
artifact. Inaddition,exceptforchangestoexisting
artifacts, itispossiblethatanorganizationmayincor-
porateasetofnewartifactsintothelocalprocess.
Changes totasks. Stemmedfromservice-orientedarchi-
tecture,anorganizationmayseektoaggregateexisting
local tasksintoacompositetask(i.e.,aservice).Onthe
otherhand,acompositetaskcanbedecomposedinto
smaller tasks.Duetothesepossiblechangestotasks,the
specification ofatask,includingtheinput,output,and
pre/post-conditionsofthetask,issubjecttoreflecting
the changes –.
Changes tobusinessrules. Businessrulescanbechanged
due tothestructuralchangesofartifacts,thespecifica-
tion changesoftasks,andthechangesoftheprocess
logic. Itisworthnotingthatachangemayaffectan
existinginteractionbehaviorbetweenartifacts.
Next,wedefinethree changeoperators that canbeusedto
expresswhatandhowtheabove-mentionedthreetypesof
changecanbeachieved.Asaforementioned,inthisarticlewe
onlyfocusonthebehavioraspectofartifact-centricbusiness
processes.Werestrictourdiscussioninbehavioralchangesof
localprocesses.Therefore,forsimplicity,weassumethat
capturingthechangeofabusinessrulecanreflectthechange
of artifact(s)andtask(s)involvedinthisrule.Thismakes
sense astheassociationsbetweenartifactsandtasksare
defined inthepre/post-conditionsandactions,respectively,
in businessrules.Inthecaseofaddinganewartifacttoalocal
process,wecanderivethelifecycleofthenewartifactandits
interactionfromtheaddedbusinessrulesthatareusedto
inducethestatetransitionoftheartifactandthesyncrules
thatareusedtosynchronizeother existingartifact(s)withit,
respectively.
Definition 25. (Change operators).Let Π^ l
¼ ðZl; Vl; Rl
Þ be
a localACPmodeloforganizationrolelinthecollaboration.
An organizationcanchangeitsownlocalprocessby
applyingthefollowingchangeoperatorsoverbusiness
rules Rl.
Add operator ðRþ Þ. Wewrite Rþ ðrÞ to meanthatnew
business rulerisaddedintoR,i.e., Rþ ðrÞ ¼ Rl
[ frg.
Delete operator ðR Þ. Wewrite R ðrÞ to meanthat
existingbusinessrulerisdeletedfromR,i.e.,
R ðrÞ ¼ Rl
frg.
Replaceoperator (R%). Wewrite R%ðrx; ryÞ tomeanthat
existingbusinessrulerx is replacedbynewbusiness
rule ry in R,i.e., R%ðrx; ryÞ ¼ Rl
[ fryg frxg.
It isnotedthatthereplaceoperatoridenticallyperforms
as thecombinationoftheaddoperatorandthedelete
operator;however,itprovidesbettertraceabilityofchanges
by maintainingtherelationforthereplacementofanold
business rulewithanewbusinessrule.
Definition 26. (Modified localACPmodel,processchange
function (pc)).Let Π^ l
¼ ðZl; Vl; Rl
Þ be a local ACPmodel of
role l.Wecanobtain modified localACPmodel Π^ l0
from Π^ l
by applying processchangefunctionpc Π^ l :Π^ l
X-Π^ l0
where
X is aunionsetof changeoperationsRþ, R, andR% that
perform onsomebusinessrulesinRl.
Next,weexplaintheconceptofprivateviewandhowit
can beusedtovalidatethechangesoflocalprocess.

5.2. Privateviewsandchangevalidation
In theoverallpicture,wevalidatethechangesoflocal
processbycheckingwhetherthe B-consistency of the
modified inter-organizationalbusinessprocess(afterlocal
processchangesapplied)andtheagreedpublicviewcanbe
preserved.A privateview of anorganizationisusedto
capturethemodifiedlocalprocessforthepurposeoflocally
checkingwhetherthelocalprocessisstillabletoprovide
what promisedintheagreedcontract,i.e.,publicview.We
illustrateanoverviewofprocesschangevalidationin
Fig. 18.
Next,wedefinethe privateview of aparticularorgani-
zation roleinthecollaborationbasedontheagreedpublic
view.Basedoneachversionoflocalprocesschanges,each
role hasacorrespondingprivateviewthatcapturesits
(modified) local ACPmodel plus abstractsharedartifacts
defined inthepublicview.
Definition 27. (Privateview).Let paΠ^ ¼ ðZp; Vp; Rp; Lp; γpÞ
be apublicviewofACP-imodel Π^ and Π^ l
¼ ðZl; Vl; Rl
Þ be a
local ACPmodelofrole lALp. The privateview of role l can
be definedby privateviewmapping function pv: Zx
[ Vx
[ Rx
[ γx-ðZp
[ Zl
Þ [ Vl
[ ðRp
[ Rl
Þ [ Lp
[ γp such thatthe
followingshold.
each abstractsharedartifactin Zp existsin Zx, i.e.,
8CiAfCAZp
j γpðCÞ

41g; (CjAZx; pvðCjÞ ¼ Ci γxðCjÞ ¼ γp ðCiÞ
each localartifactin Zl (not in Zp) existsin Zx, i.e.,
8CiAfCAZl
jjγpðCÞj ¼ 1g; (CjAZx; pvðCjÞ ¼ Ci
γxðCjÞ ¼ l
each taskin Vl existsin Vx, i.e.,
8viAVl; (vjAVx; pvðvjÞ ¼ vi γxðvjÞ ¼ l
each businessrulein Rl existsin Rx, i.e.,
8riARl; (rjARx; pvðrjÞ ¼ ri;
each abstractbusinessrulein Rp that isnotusedforthe
synchronizationbetweenanabstractsharedartifactin
Zp and alocalartifactin Zl existsin Rx, i.e.,
8riAfrARp
jl=2γpðrÞg; (rjARx; pvðrjÞ ¼ ri
Notethatwemayusethetermprivateviewforthe
lifecycleofthisprivateviewinanunambiguouscontext.
Example 18. Fig. 19 depicts thelifecyclesofartifactsinthe
privateviewoftheoriginallocalprocessofSupplier
(Π^ Supplier
1 ) whichisextractedfromthecompletepurchasing
processshownin Fig. 1. Suchprivateviewcanbecon-
structedbasedonthepublicviewshownin Fig. 5. Apart
fromthelocalartifacts PL and DN, comparedwiththe
public view,wecanseelocalprocessdetails(ingray-
shaded areas)ofsharedartifacts PO, SO, and IV.
Example 19. Now,considerthecasethatifSupplierwants
tochangeitslocalprocessbasedontheexistingone(cf.
Fig. 19). Theresultofchangesisillustratedinprivateview
Π^ Supplier
2 in Fig. 20. Sincethe IL artifact isaddedintothelocal
process,wecanseesomesynchronizationbetweenexisting
artifact PL and newartifact IL, aswellasthechangeof
state’s namesof PL (from checking to scheduled, from out of
stock to unavailable, andfrom in stock to picking). Existing
business rulesthatcorrespondtothesechangesare
affectedandneededtobeadjustedaccordingly.Obviously,
a newsetofbusinessrulesisneededtoexpressthe
lifecycleoftheaddedartifact.Thissetincludessyncrules
that areusedforthesynchronizationbetween PL and IL.
Next,wedefine processconformance and itsconditions
that canbeusedtocheckwhetherchangesinlocalprocess
can beimplementedwhilepreservingthecorrectnessand
consistencyoftheoverallprocess.Basically,wereusethe
definition of B-consistency to define processconformance for
Fig. 18. An overviewofprivateviewsandviewconformance.

consistentlocalprocesschangesastosatisfythefollowing
statements.
Changesshouldnotleadtoanunsoundglobalprocess,
i.e., themodifiedglobalprocessshouldbeabletoreach
its goalstatesasitsoriginalglobalprocessdoes,and,
Changesshouldbeguaranteedthatthe B-consistency of
the modifiedglobalprocessanditsoriginalglobal
processispreserved.
As anagreedpublicviewisconstructedforthecolla-
borationwhichactslikeacontract,sowecanexpress
consistent processchanges by meansofnotbreakingthe
original publicview.Inotherwords,themodified ACP-i
model must beconsistentwiththeagreedpublicview.
Regardingthebehavioralequivalencenotioninprocess
algebras [9], wecansaythatourapproachforconsistent
processchangespreservesthecongruencepropertyofthe
modified localprocessanditsbaselocalprocess,i.e.,they
can behaveinterchangeablywithoutaffectingtheoverall
process.
Definition 28. (Processconformance, F). Let Π^ ¼ ðZ;
V; R; L; γÞ be anACP-imodeland paΠ^ be its public view.
Let pv Π^ l be aprivateviewof local ACPmodel Π^ l
for role lAL.
Wesaythat Π^ l
conformspa Π^ , writtenas Π^ l
FpaΠ^ , iffthe
Picking List(PL)
Purchase Order(PO)
confirmed
canceled
Out ofstock
closed
Shipping Order(SO)
In transit
Invoice (IV)
approving
acquiring
accepted filled
checking Instock
Delivery Note(DN)
prepared
transferring
dispatched
billing
issued
cleared
sent
unpaid
clearing
arrived
delivering
ready toship
created scheduled
Fig. 19. Supplier’s privateview Π^ Supplier
1 .
Picking List(PL)
Purchase Order(PO)
confirmed
canceled
unavailable
closed
Shipping Order(SO)
Invoice (IV)
approving
acquiring
accepted filled
scheduled picking
Delivery Note(DN)
prepared
transferring
dispatched
billing
issued
cleared
sent
unpaid
clearing
Inventory List(IL)
checking
ready topick
sourcing
canceled
delivering
ready toship
In transit created scheduled arrived
Fig. 20. Supplier’s modifiedprivateview Π^ Supplier
2 .

A view framework for modeling and change validation of artifact centric inter-organizational business processes

A view framework for modeling and change validation of artifact centric inter-organizational business processes

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A view framework for modeling and change validation of artifact centric inter-organizational business processes