A Projection-Stable Grammatical Model for the Distributed Execution of Administrative Processes with Emphasis on Actors' Views
Milliam Maxime Zekeng Ndadji, Maurice Tchoupé Tchendji, Clémentin Tayou Djamegni, Didier Parigot
AA Projection-Stable Grammatical Model for the DistributedExecution of Administrative Processes with Emphasis onActors’ Views
Milliam Maxime Z
EKENG N DADJI a,b, ∗ , Maurice T CHOUPÉ T CHENDJI a,b ,Clémentin T
AYOU D JAMEGNI a , Didier P ARIGOT c a Department of Mathematics and Computer ScienceUniversity of Dschang, PO Box 67, Dschang-Cameroon b FUCHSIA Research Associated Team, https://project.inria.fr/fuchsia/ c Inria, Sophia Antipolis, France
Abstract
During the last two decades, the decentralized execution of business processeshas been one of the main research topics in Business Process Management. Sev-eral models (languages) for processes’ specification in order to facilitate their dis-tributed execution, have been proposed. LSAWfP is among the most recent in thisarea: it helps to specify administrative processes with grammatical models indicat-ing, in addition to their fundamental elements, the permissions (reading, writingand execution) of each actor in relation to each of their tasks. In this paper, wepresent a model for a completely decentralized and artifact-centric execution ofadministrative processes specified using LSAWfP. The presented model puts par-ticular emphasis on actors’ views: it then allows the confidential execution of cer-tain tasks by ensuring that, each actor potentially has only a partial perception ofthe processes’ global execution states. To accomplish this, the model is based onthree projection algorithms allowing to partially replicate the processes’ global ex-ecution states at a given moment, to consistently update the obtained partial statesand to deduce new coherent global states. The proposal of these three algorithms,the proof of underlying mathematical tools’ stability and a proposal of their imple-mentation, are this paper’s main contributions.
Keywords:
Administrative Processes, Projection, Grammars, Views, LSAWfP. ∗ Corresponding author
Email addresses: [email protected] (Milliam Maxime Z
EKENG N DADJI ), [email protected] (Maurice T CHOUPÉ T CHENDJI ), [email protected] (Clémentin T AYOU D JAMEGNI ), [email protected] (Didier P ARIGOT ) Preprint submitted to arXiv.org February 23, 2021 a r X i v : . [ c s . S E ] F e b . Introduction Administrative business processes are those of which all cases are known andpredictable; that is to say, tasks sequencing rules are simple and clearly defined[1, 2]: they are the most frequently encountered in practice [3, 4] (the peer reviewprocess [5, 6, 7, 8, 9], the insurance claims process [10, 11], etc.). In its mostwidespread approach, Business Process Management (BPM) technology breaksdown the automation of a given business process to its formal specification (mod-elling) in a workflow language [4]. The resulting process (workflow) model gener-ally describes all the process’s tasks, the control flow that link them (routing) andthe actors in charge of executing them [3].For the decentralized execution of an administrative process described in anyworkflow language, one can imagine a distributed
Workflow Management System (WfMS) made up of several reactive agents or peers, driven by human agents (ac-tors in charge of executing tasks), coordinating with each other using an artifactthat they cooperatively edit. In fact, the distributed execution of an administrativeprocess is similar to the cooperative edition of a form that has to circulate from siteto site (mobile form) in order to be edited by the different actors of the process.Upon its arrival on a site, the actor associated with the site must be able to exam-ine it and deduce without ambiguity, the already edited fields (these correspond tothe already executed tasks of the process), the fields that he must immediately edit(these correspond to the ready tasks that he must execute), and possibly, the sitesto which he must return/redirect the form for further processing at the end of itsedition. It is easy to imagine that there could be forms with independent fields thatneed to be filled in by different actors. In this case, in order to speed up processing,it is acceptable that at a given time, there may be several replicas of the form thatare simultaneously edited in the system.A major characteristic of administrative processes is confidentiality: not allactors in an administrative process are necessarily aware of all processing and/ordata generated in the process. It is therefore natural to assume that the form that ispresented to an actor for editing on a site is only a potentially partial replica of theglobal form ; this (partial) replica only contains information (relating to processingand data) that is of proven interest to the considered actor. Once a partial replica ofa form has been received, it is essential to ensure that all editing actions on it canbe consistently integrated into the global form. In order to satisfy this constraint, it The global form contains all the data already filled in so far by the various actors in the system.It therefore gives the process’ global execution status at a given moment, by explicitly highlightingthe fields already edited, those ready to be immediately edited, and those that will be edited later (inthe case of dependencies between fields).
2s sufficient for each actor to have a local "supervisor" who must control his editingactions.The form described in the two paragraphs above can be seen as a structureddocument (a tree) circulating from site to site, to be extended by cooperative edi-tions made at the level of its leaves (positive edition ). The nodes of this treetherefore represent either the tasks already executed, or those ready to be executed;moreover, the relations between nodes (father-son, brother-brother) correspond ex-actly to the ordering of tasks. This tree is called " artifact " in the artifact-centricapproach to business process modelling.Based on the cooperative editing model of structured documents studied in theworks of Badouel et al. [14, 15, 16, 17, 18, 19], we propose in this paper, a modelfor the distributed execution of administrative processes (cooperative edition of ar-tifacts) that relies on algorithms to obtain : (1) partial replicas of the global artifact( artifact projection algorithm); these contain only the information relevant to theconsidered actors; (2) local models that constrain local editing actions on localartifacts ( model projection algorithm), so as to ensure that these are always "ex-pandable" as editing actions (updates) on the global artifact ( expansion algorithm).The proposed execution model applies only to process models obtained using thelanguage LSAWfP ( A Language for the Specification of Administrative WorkflowProcesses ) [7, 8, 9]. LSAWfP is a new language designed for the specification(using a variant of attributed grammars) of administrative processes with particularemphasis placed on the modelling (using views) of the perceptions that the variousactors have on processes and their data. The specification of a particular process inthis language is given by a triplet ( a Grammatical Model of Administrative Work-flow Process - GMAWfP -) W f = ( G , L P k , L A k ) wherein, G is the model of tasksand their sequencing, L P k and L A k represent respectively the list of actors and theiraccreditations . If we consider a GMAWfP W f = ( G , L P k , L A k ) to be executed ina decentralized manner, then the main contributions of this paper are as follows:1) The proposal of algorithms for:• artifacts’ projection ; which, given an artifact t that conforms to the (global)model G and the accreditation in reading A A i ( r ) (known as view and denoted V i ) of an actor A i , allows to find its partial replica t V i ;• model’s projection ; which permits, from a view V i and a global model G , toderive a local model G V i . G V i will guide the actions carried out by a given In a positive edition, no information is erased [12, 13]. Editing actions on the document havethe effect of making the tree representing it grow, by adding sub-trees at the level of its leaves. The accreditation of a given actor provides information on its rights (permissions) relatively toeach sort (task) of the studied process. G .• expansion-pruning ; which enable the inverse projection of a partial replica t ma j V i updated by a given actor A i according to a local GMWf G V i ; the goal isto integrate the contributions made by the local actor into an artifact t f thatconforms to the global model G .2) A study of stability properties of artifacts and their model, when using the pro-posed algorithms.3) A Haskell implementation of the proposed algorithms. Organization of the manuscript : in the remainder of this manuscript, we brieflypresent the LSAWfP language and an example of a process modelled using it (sec.2.2). We then present the artifact-centric model of process execution consideredin this paper, in order to motivate the need to propose stable projection algorithms(sec. 2.3). We continue by proposing versions of the three projection algorithmscovered in this paper as well as a study of some of their properties (sec. 3). We endwith a discussion and a conclusion.
2. On the Modelling and the Execution of Administrative Business Processesusing LSAWfP
Several tools have been developed to address process modelling. Among themost well-known are the BPMN standard (
Business Process Model and Notation )[20] which uses a formalism derived from that of statecharts, and the YAWL lan-guage (
Yet Another Workflow Language ) [21, 3, 22] based on Petri nets. Despitethe significant research progress around these workflow languages, they are oftencriticized for having a much too great expressiveness compared to the needs ofprofessionals in the field [23], for not being based on solid mathematical founda-tions and/or for not being intuitive [24]: This justifies the emergence of severalother languages such as LSAWfP [7, 8, 9]. In this section, we present the LSAWfPlanguage and its illustration: the specification of the administrative process usedas a running example along this paper. The artifact-centric execution model ofLSAWfP’s specifications is also presented in order to motivate the current work.
The peer-review process is a commonly used example of business process toillustrate workflow languages [5, 6, 7, 8, 9]. We choose it in this manuscript be-cause it is easy to describe and (that’s the most important) it perfectly illustrates4he concepts that we handle. The description that we consider is the same as theone in [7]: the process involves four actors (an editor in chief - EC -, an associatededitor - AE - and two referees - R R EC receives the paper;• Upon receipt, the EC pre-validates the paper (let us call this task " A " );after the pre-validation, he can accept or reject the paper for various reasons(subject of minor interest, paper not within the journal scope, non-compliantformat, etc.);• If he rejects the paper, he writes a report ( task " B " ) then notifies the corre-sponding author ( task " D " ) and the process ends;• Otherwise, he chooses an AE and sends him the paper;• The AE prepares the manuscript ( task " C " ) forms a referees committee (twomembers in our case) and then triggers the peer-review process ( task " E " );• Each referee reads, seriously evaluates the paper ( tasks " G " and " G " )and sends back a report ( tasks " H " and " H " ) and a message ( tasks " I " and " I " ) to the AE ;• After receiving reports from all referees, the AE takes a decision and informsthe EC ( task " F " ) who sends the final decision to the corresponding author( task " D " ). LSAWfP is a recent language specifically designed for administrative processmodelling. It relies on a variant of attributed grammars to provide a frameworkfor the modelling of the main conceptual aspects of such processes: these are theaspects related to tasks’ scheduling (the lifecycle model ), to data consumed andproduced by tasks (the informational model ), and to resources in charge of execut-ing tasks (the organizational model ) [25]. In addition, LSAWfP puts a particularemphasis on the modelling (using views) of the perceptions that the various stake-holders have on processes and their data in order to guarantee confidentiality. Tomodel a given process with LSAWfP, four key steps must be followed: (1) modelthe process scenarios using annotated trees and (2) derive from annotated trees, anabstract grammar which will be used as lifecycle model; then (3) identify the actorsinvolved in the process execution and (4) establish the role played by each of themusing a list of accreditations. 5 .2.1. Modelling Process Scenarios using Artifacts
LSAWfP is founded on the principle that, by definition, all execution scenarios,all actors and the role they play in relation to tasks of a given administrative pro-cess P ad , are known in advance. LSAWfP therefore proposes to model each P ad ’sexecution scenario using an annotated tree t i called target artifact . In such a tree,each node (labelled X i ) potentially corresponds to a task X i of P ad and each hier-archical decomposition (a node and its sons) corresponds to a scheduling: the taskassociated with the parent node must be executed before those associated with theson nodes; the latter must be executed according to an order - parallel or sequential- that can be specified by particular annotations " (cid:35) " (is sequential to) and " (cid:107) " (isparallel to) which will be applied to each hierarchical decomposition. The annota-tion " (cid:35) " (resp. " (cid:107) ") reflects the fact that the tasks associated with the son nodes ofthe decomposition must (resp. can) be executed in sequence (resp. in parallel).For the running example (the peer-review process), there is only two executionscenarios: the one in which the EC immediately rejects the paper and the one inwhich the paper goes through the validation process. These can be modelled usingthe two artifacts art and art in figure 1. In particular, we can see that art showshow the task "Receipt and pre-validation of a submitted paper" assigned to the EC ,and associated with the symbol A (see sec. 2.1), must be executed before tasksassociated with the symbols B and D that are to be executed in sequence. Figure 1: Example of target artifacts for a given process (peer-review process)
After modelling the scenarios of the studied process using target artifacts,LSAWfP suggests to extract from them, an abstract grammar called a
GrammaticalModel of Workflow (GMWf) . This is done by simply substituting the set of targetartifacts by a grammar G (a GMWf) in which, each symbol refers to a task and,each production p is of one of the following two forms: p : X → X (cid:35) . . . (cid:35) X n or p : X → X (cid:107) . . . (cid:107) X n . These two forms of productions perfectly models the two6ypes of ordering (parallel or sequential) retained in the design of the target arti-facts. In this case, each target artifact t i is conform to G and we note t i ∴ G ; alsothe root symbols of the different target artifacts make up the set of axioms of G . AGMWf can then be formally defined as follows: Definition 1. A Grammatical Model of Workflow (GMWf) is defined by G =( S , P , A ) where : • S is a finite set of grammatical symbols or sorts corresponding to various tasks to be executed in the studied business process; • A ⊆ S is a finite set of particular symbols called axioms , representing tasksthat can start an execution scenario (roots of target artifacts), and • P ⊆ S × S ∗ is a finite set of productions decorated by the annotations " (cid:35) "(is sequential to) and " (cid:107) " (is parallel to): they are precedence rules . Aproduction P = (cid:0) X P ( ) , X P ( ) , · · · X P ( | P | ) (cid:1) is either of the form P : X → X (cid:35) . . . (cid:35) X | P | , or of the form P : X → X (cid:107) . . . (cid:107) X | P | and | P | designates the lengthof P right-hand side. A production with the symbol X as left-hand side iscalled a X-production. Considering the case of the peer-review process whose target artifacts are rep-resented in figure 1, the derived GMWf is G = ( S , P , A ) in which the set S of gram-matical symbols is S = { A , B , C , D , E , F , G , G , H , H , I , I } (see sec. 2.1); theonly initial task (axiom) is A (then A = { A } ) and the set P of productions is: P : A → B (cid:35) D P : A → C (cid:35) D P : C → E (cid:35) F P : E → G (cid:107) G P : G → H (cid:35) I P : G → H (cid:35) I P : B → ε P : D → ε P : F → ε P : H → ε P : I → ε P : H → ε P : I → ε The identification of the actors taking part in the execution of the process iseasily done with the help of its textual description. For example, according tothe description of the peer-review process, four ( k =
4) actors participate in itsexecution: an editor in chief ( EC ), an associated editor ( AE ) and two referees ( R R L P k = { EC , AE , R , R } . LSAWfP proposes a mechanism called accreditation , inspired by the nomen-clature of rights used in Unix-like systems, to ensure better coordination betweenactors and to eventually guarantee the confidentiality of certain actions and data.7he accreditation of a given actor provides information on its rights (permissions)relatively to each sort (task) of the studied process’s GMWf. There is three typesof accreditation: The accreditation in reading (r) : an actor accredited in reading on sort X musthave free access to its execution state (data generated during its execution). The setof sorts on which an actor is accredited in reading is called his view . Any sort X belonging to a given view V i ( X ∈ V i ) is said to be visible , and those not belongingto it are said to be invisible . The accreditation in writing (w) : an actor accredited in writing on sort X canexecute the associated task . Any actor accredited in writing on a sort is accreditedin reading on it. The accreditation in execution (x) : an actor accredited in execution on sort X is allowed to ask the actor who is accredited in writing in it, to execute it. Moreformally, an accreditation is defined as follows: Definition 2. An accreditation A A i defined on the set S of grammatical symbols foran actor A i , is a triplet A A i = (cid:0) A A i ( r ) , A A i ( w ) , A A i ( x ) (cid:1) such that, A A i ( r ) ⊆ S also called view of actor A i , is the set of symbols on which A i is accredited in reading, A A i ( w ) ⊆ A A i ( r ) is the set of symbols on which A i is accredited in writing and A A i ( x ) ⊆ S isthe set of symbols on which A i is accredited in execution. From the task assignment for the peer-review process in the running example, itfollows that the accreditation in writing of the EC is A EC ( w ) = { A , B , D } . Moreover,since he can only execute task D if task C (executed by the AE ) is already executed(see artifacts art and art , fig. 1), he must be accredited in execution on C tobe able to request its execution; therefore, we have A EC ( x ) = { C } . In addition, inorder to be able to access all the information on the progress of the peer-reviewevaluation (task C ) and synthesize the right decision to be returned, the EC mustbe able to consult reports (tasks I I
2) and messages (tasks H H
2) ofthe referees, as well as the decision made by the AE (task F ). These tasks, inaddition to A EC ( w ) constitute the set A EC ( r ) = V EC = { A , B , C , D , H , H , I , I , F } of tasks on which he is accredited in reading. Doing so for each of the other actorsleads to the deductions of the accreditations represented in the table 1 and we have L A k = { A EC , A AE , A R , A R } . Finally the Grammatical Model of Administrative Workflow Process : withLSAWfP, the modelling of a process results in a triplet W f = ( G , L P k , L A k ) (called Let’s recall that the execution of a task is assimilated to the edition (extension) of a particularnode in an artifact. Remember: any actor accredited in writing on a sort is accredited in reading on it. ctor Accreditation Editor in Chief ( EC ) A EC = ( { A , B , C , D , H , H , I , I , F } , { A , B , D } , { C } ) Associated Editor( AE ) A AE = ( { A , C , E , F , H , H , I , I } , { C , E , F } , { G , G } ) First referee ( R A R = ( { C , G , H , I } , { G , H , I } , /0 ) Second referee ( R A R = ( { C , G , H , I } , { G , H , I } , /0 ) Table 1: Accreditations of the different actors taking part in the peer-review process. a Grammatical Model of Administrative Workflow Process - GMAWfP -) wherein, G is the GMWf, L P k is the list of actors and L A k is the list of their accreditations. The artifact-centric paradigm, emerged in the early 2000s, has become the mostexploited current of thought for process modelling and execution (workflow man-agement) over the last two decades [3]. Several works [26, 27, 28, 29, 30, 31, 32,33, 34] have been undertaken to develop this paradigm. According to it, workflowmanagement focuses on both automated processes and data manipulated using theconcept of business artifact . A business artifact is considered as a document thatconveys all the information concerning a particular case of execution of a givenbusiness process, from its inception in the system to its termination. In this sec-tion, we present an artifact-centric model for the distributed execution of GMAWfPinspired by the work of Badouel et al. on cooperative editing of structured docu-ments [14, 15, 16, 18, 19]. We begin by presenting individually, the key conceptsof the execution model, before examining the overall behaviour of the distributedsystem.
The Execution Environment : to execute a given GMAWfP in a decentralizedmode, we consider a completely decentralized (P2P) WfMS model (which we call
P2P-WfMS-View ) whose instances (the peers) are installed on the sites of the var-ious actors involved in processes execution. During the process execution, thesepeers communicate (sending/receiving requests/responses) by exchanging copiesof a (global) artifact said to be under execution. Such an artifact provides informa-tion on already executed tasks and on those ready to be executed.As in the work of Badouel et al. [14, 15, 16, 18, 19], we represent an artifactunder execution by a tree (a structured document) that contains buds . These indi-cate at a moment, the only places where contributions are expected. A bud can beeither unlocked or locked depending on whether the corresponding task (node) isready to be executed (edited) or not. Buds are typed; a bud of type X ∈ S is a leaf9ode labelled either by X ω or by X ω depending on its state ( locked or unlocked )(see fig. 2). The local actions of a given actor will therefore have the effect ofextending (editing) its received copy of the (global) artifact by developing, throughappropriate productions, the different unlocked buds it contains. Figure 2: An intentional representation of an annotated artifact containing buds.
The Confidential Execution of Certain Tasks : for confidentiality reasons, eachactor acts on a potentially partial replica of the local copy of the (global) artifact:this partial replica contains only the information to which the concerned actor canhave access. Technically, a partial replica t V i of an artifact t is obtained by projec-tion (using an operator π said of artifact projection ) of t according to the view V i of the concerned actor: we note t V i = π V i ( t ) . The Need of a Local GMWf at each Site : since the local actions of a particularactor depend on his perception of the process, it is necessary to control them inorder not only to preserve the possible confidentiality of certain tasks, but also toensure the consistency of local updates. To do this, one must derive a local GMWfon each site, by projecting the global GMWf according to the view of the localactor (
GMWf projection ). This projection is carried out using Π operator and theGMWf obtained is noted G V i = Π V i ( G ) . The Expansion Operation : still with the aim of ensuring system convergence,the contributions made by a given actor and contained in an updated partial replica t ma j V i , must be integrated into the local copy of the (global) artifact before any syn-chronization between peers. It is therefore necessary to be able to merge these twoartifacts, which are based on two different models. We find here, a version of the expansion problem as formulated in [14]. Globally then, before the execution of a given process, peers are configuredusing its GMAWfP ( W f = ( G , L P k , L A k )) . From the global GMWf G and the view V i of the local actor, each peer derives by projection, a local GMWf G V i = Π V i ( G ) .Then, the execution of a process case is triggered when an artifact t is introducedinto the system (on the appropriate peer); this artifact is actually an unlocked bud10f the type of one axiom A G ∈ A (initial task) of the (global) GMWf G (see fig. 3).During execution, peers synchronize themselves by exchanging their local copiesof the artifact being executed.After receiving an artifact t ∴ G on a given peer, the latter projects it (see Peer i in fig. 3) according to the local view V i . The obtained partial replica t V i ∴ G V i is then completed (edited) when needed: the result of this edition is an artifact t ma j V i ∴ G V i such as t ma j V i is an update of t V i ( t ma j V i ≥ t V i ).At the end of the completion, the expansion-pruning of the obtained updatedpartial replica t ma j V i ∴ G V i is made in order to obtain the updated configuration t f ∴ G of the (global) artifact local copy (see Peer i in fig. 3). If the resultingconfiguration shows that the process should be continued at other sites , then repli-cas of the artifact are sent to them. Else , a replica is returned to the peer fromwhom the artifact was previously received. Figure 3: Overview of the distributed execution of a given process.
3. Projection Algorithms for the Distributed Execution of GMAWfP
The GMAWfP execution model is mainly based on three algorithms: artifactprojection , GMWf projection and expansion . In this section, we propose versions ofthese algorithms as well as a study of some of their mathematical properties guar-anteeing the correction of the execution model, and the coherence of the distributedsystem formed by the peers in charge of the execution of a given GMAWfP. This is the case when the artifact contains buds created on the current peer and whose actorsaccredited in writing are on distant peers. The artifact is complete (it no longer contains buds), or semi-complete (it contains buds thatwere created on other peers and on which, the actor on the current peer is not accredited in writing). .1. The Artifact Projection Algorithm3.1.1. The Algorithm Technically, the projection t V i of an artifact t according to the view V i = A A i ( r ) is obtained by deleting in t all nodes whose types do not belong to V i (all invisiblenodes). In our case, the main challenges in this operation are: (1) nodes of t V i must preserve the previously existing execution order betweenthem in t , (2) t V i must be build by using exclusively the only two forms of productionretained for GMWf and (3) t V i must be unique in order to ensure the continuation of process execution(see sec. 2.3.2).The projection operation is noted π . Inspired by the one proposed in [14], itprojects an artifact by preserving the hierarchy (father-son relationship) betweennodes of the artifact (it thus meets challenge (1) ); but in addition, it inserts into theprojected artifact when necessary, new additional (re)structuring symbols (acces-sible in reading and writing by the agent for whom the projection is made). Thisenables it to meet challenge (2) . The details of how to accomplish the challenge (3) are outlined immediately after the algorithm (algorithm 1) is presented. Figure 4: Example of projections made on an artifact and partial replicas obtained.
Figure 4 illustrates the projection of an artifact of the peer-review process rel-atively to the R EC (Editor in Chief) views. Note the presencein t V EC of new (re)structuring symbols (in gray). These last ones make it possibleto avoid introducing in t V EC , the production p : C → H (cid:35) I (cid:107) H (cid:35) I (cid:35) F whose12orm does not correspond to the two forms of production retained for the GMWfwriting .Let’s consider an artifact t and note by n = X [ t , . . . , t m ] a node of t labelled withthe symbol X and having m sub-artifacts t , . . . , t m . Note also by p n , the productionof the GMWf that was used to extend node n ; the type of p n is either sequential (i.e. p n is of the form p n : X → X (cid:35) . . . (cid:35) X m where X , . . . , X m are the roots of thesub-artifacts t , . . . , t m ) or parallel ( p n : X → X (cid:107) . . . (cid:107) X m ). Concretely, to project t according to a given view V (i.e to find projs t = π V ( t ) ), a depth path of t isperformed and invisible nodes are erased or replaced by new nodes associated with(re)structuring symbols to preserve the subtree structure. To do so, the recursiveprocessing presented in algorithm 1, is applied to the root node n = X [ t , . . . , t m ] of t . Algorithm 1
Algorithm to project a given artifact according to a given view. • If symbol X is visible ( X ∈ V ) then : n is kept in the artifact; For each sub-artifact t i of n , having node n i = X i (cid:2) t i , . . . , t i k (cid:3) as root (of which p n i isthe production that was used to extend it), the following processing is applied : a. The projection of t i according to V is done. We obtain the list projs t i = π V ( t i ) = (cid:110) t i V , . . . , t i V l (cid:111) ; b. If the type of p n i is the same as the type of p n or the projection of t i has producedno more than one artifact ( | projs t i | ≤ t i by artifacts t i V , . . . , t i V l ofthe list projs t i ;Otherwise, a new (re)structuring symbol S i is introduced and we replace the sub-artifact t i with a new artifact new _ t i whose root node is n t i = S i (cid:104) t i V , . . . , t i V l (cid:105) ; If the list of new sub-artifacts of n contains only one element t having n = S (cid:104) t V , . . . , t V l (cid:105) (with S a newly created (re)structuring symbol) as root node, wereplace in this one, t by the sub-artifacts t V , . . . , t V l of n . This removes a non-important (re)structuring symbol S . • Else , n is deleted and the result of the projection ( projs t ) is the union of the projec-tions of each of its sub-artifacts: projs t = π V ( t ) = (cid:83) mi = π V ( t i ) Note that the algorithm described here applies to all artifacts (including thosecontaining buds) because there is no need to apply any special treatment (lockingor unlocking) on buds: they must also be just erased or kept in the artifact to Note that this production specifies in its right-hand side that we must have parallel and sequentialtreatments. Inserting S S S p in four productions p C → S (cid:35) F , p S → S (cid:107) S p S → H (cid:35) I p S → H (cid:35) I (3) , we make the following assumption: GMAWfP manipulated in this work are such that all actors are accred-ited in reading on the GMWf axioms ( axioms’ visibility assumption ). The designer must therefore ensure that all actors are accredited in reading on allGMWf axioms. To do this, after modelling a process P ad and obtaining its GMWf G = ( S , P , A ) , it is sufficient (if necessary) to create a new axiom A G on which, allactors will be accredited in reading, and to associate it with new unit productions pa : A G → X a where, X a ∈ A is a symbol labelling the root of a target artifact.Moreover, the designer of the GMWf must statically choose the actor responsiblefor initiating the process. This actor will therefore be the only one to possess anaccreditation in writing on the new axiom A G . Proposition 3.
For all GMAWfP W f = ( G , L P k , L A k ) verifying the axioms’ visibil-ity assumption, the projection of an artifact t which is conform to its GMWf (t ∴ G )according to a given view V , results in a single artifact t V = π V ( t ) (stability prop-erty of artifacts through the usage of π ).Proof. Let’s show that π V ( t ) produces a single tree t V which is an artifact. Notethat the only case in which the projection of an artifact t according to a view V pro-duces a forest, is when the root node of t is associated with an invisible symbol X ( X / ∈ V ). Knowing that t ∴ G and that W f validates the axioms’ visibility assump-tion, it is deduced that the root node of t is labelled by one of the axioms A G of G and that A G ∈ V (hence the uniqueness of the produced tree). Since the projectionoperation preserves the form of productions, it is concluded that t V = π V ( t ) is anartifact. (cid:50) The goal of this algorithm is to derive by projection of a given GMWf G =( S , P , A ) according to a view V , a local GMWf G V = ( S V , P V , A V ) (we note G V = Π V ( G ) ). The proposed algorithm (algorithm 2) generates the set of target A production of a context free grammar is a unit production if it is on the form A → B , where A and B are non-terminal symbols. denoted by G then, it simply project each target artifact according to theview V , then gather the productions in the obtained partial replicas while removingthe duplicates. Algorithm 2
Algorithm to project a given GMWf according to a given view. First of all, it is necessary to generate all the target artifacts denoted by G (see note(1) below); we thus obtain a set arts G = { t , . . . , t n } ; Then, each of the target artifacts must be projected according to V . We thus obtaina set arts G V = (cid:8) t V , . . . , t V m (cid:9) (with m ≤ n because there may be duplicates; in thiscase, only one copy is kept) of artifacts partial replicas; Then, collect the different (re)structuring symbols appearing in artifacts of arts G V ,making sure to remove duplicates (see note (2) below) and to accordingly update theartifacts and the set arts G V . We thus obtain a set S V Struc of symbols and a final set arts G V = (cid:8) t V , . . . , t V l (cid:9) (with l ≤ m ) of artifacts. These are exactly the only ones thatmust be conform to the searched GMWf G V . So we call them, local target artifactsfor the view V ; At this stage, it is time to collect all the productions that made it possible to buildeach of the local target artifacts for the view V . We obtain a set P V of distinct pro-ductions. The searched local GMWf G V = ( S V , P V , A V ) is such as : a. its set of symbols is S V = V ∪ S V Struc ; b. its set of productions is P V ; c. its axioms are in A V = A Note (1):
To generate all the target artifacts denoted by a GMWf G = ( S , P , A ) , onejust has to use the set of productions to generate the set of artifacts having one of theaxiom A G ∈ A as root. In fact, for each axiom A G , it should be considered that everyA G -production P = ( A G , X · · · X n ) induces artifacts { t , . . . , t m } such as: the root nodeof each t i is labelled A G and has as its sons, a set of artifacts { t i , . . . , t i n } , part ofthe Cartesian product of the sets of artifacts generated when considering each symbolX , · · · , X n as root node. Note (2):
In this case, two (re)structuring symbols are identical if for all their ap-pearances in nodes of the different artifacts of arts G V , they induce the same localscheduling. Figure 5 illustrates the research of a local model G V EC such as G V EC = Π V EC ( G ) with V EC = A EC ( r ) = { A , B , C , D , H , H , I , I , F } . Target artifacts generated from G (fig. 5(b)) are projected to obtain two local target artifacts for the view V EC (fig. This generation is necessary because each peer is only configured using the GMWf G and there-fore does not possess all its target artifacts, even though the designer produced G using these artifacts. Figure 5: Example of projection of a GMWf according to a given view.
The GMWf projection algorithm presented here only works for GMWf that donot allow recursive symbols . We therefore assume that: For the execution model presented in this paper, the manipulated GMAWfPare those whose GMWf do not contain recursive symbols ( non-recursiveGMWf assumption ) .With this assumption, it is no longer possible to express iterative routing betweenprocess tasks (in the general case); except in cases where the maximum number ofiterations is known in advance. Proposition 4.
For all GMAWfP W f = ( G , L P k , L A k ) verifying the axioms’ visi-bility and the non-recursivity of GMWf assumptions, the projection of its GMWf G = ( S , P , A ) according to a given view V , is a GMWf G V = Π V ( G ) for aGMAWfP W f V verifying the assumptions of axiom visibility and non-recursivityof GMWf (stability property of GMWf through the usage of Π ). It is only in this context that all the target artifacts can be enumerated. roof. Let’s show that G V = Π V ( G ) is a GMWf for a new GMAWfP W f V = (cid:16) G V , L P k , L A V k (cid:17) that verifies the assumptions of axioms’ visibility and non-recursivityof GMWf. As W f = ( G , L P k , L A k ) validates the non-recursivity of GMWf assump-tion, the set of target artifacts ( arts G = { t , . . . , t n } ) that it denotes is finite and cantherefore be fully enumerated. Knowing further that W f validates the axioms’ visi-bility assumption, it is deduced that the set arts G V = (cid:8) t V = π V ( t ) , . . . , t V n = π V ( t n ) (cid:9) is finite and the root node of each artifact t V i is associated with an axiom A G ∈ A (see proposition 3). G V being built from the set arts G V , its axioms A V = A are vis-ible to all actors and its productions are only of the two forms retained for GMWf.In addition, each new (re)structuring symbol ( S ∈ S V Struc )) is created and used onlyonce to replace a symbol that is not visible and not recursive (by assumption) whenprojecting artifacts of arts G . The new symbols are therefore not recursive. Byreplacing in L A k the view V by V ∪ S V Struc , one obtains a new set L A V k of accredi-tations for a new GMAWfP W f V = (cid:16) G V , L P k , L A V k (cid:17) verifying the assumptions ofaxioms’ visibility and non-recursivity of GMWf. (cid:50) Proposition 5.
For all GMAWfP W f = ( G , L P k , L A k ) verifying the axioms’ visibil-ity and the non-recursivity of GMWf assumptions, the projection of an artifact twhich is conform to the GMWf G according to a given view V , is an artifact whichis conform to the projection of G according to V ( ∀ t , t ∴ G ⇒ π V ( t ) ∴ Π V ( G )) .Proof. Knowing that the considered GMAWfP W f = ( G , L P k , L A k ) verifies theaxioms’ visibility and the non-recursivity of GMWf assumptions, it is deducedthat the set of its target artifacts arts G (those who helped to build its GMWf G ) is finite and any artifact that is conform to its GMWf G is a target artifact ( ∀ t , t ∴ G ⇔ t ∈ arts G ) . Therefore, considering a given artifact t such that t isconform to G ( t ∴ G ), one knows that it is a target artifact ( t ∈ arts G ) and its pro-jection according to a given view V produces a single artifact t V = π V ( t ) (see"stability property of π ", proposition 3) such as t and t V have the same root (oneof the axioms A G ∈ A of G ). Since t is a target artifact, its projection t V (throughthe renaming of some potential (re)structuring symbols) is part of the set arts G V of artifacts that have generated G V = Π V ( G ) by applying the projection principledescribed in the algorithm 2. Therefore, the productions involved in the construc-tion of t V are all included in the set of productions of the GMWf G V = Π V ( G ) .As the set of axioms of G V is A V = A , it is deduced that A G ∈ A V and concludedthat t V ∴ G V . (cid:50) Proposition 6.
Consider a GMAWfP W f = ( G , L P k , L A k ) verifying the axioms’visibility and the non-recursivity assumptions. For all artifact t V which is conform o Π V ( G ) , it exists at least one artifact t which is conform to G such that t V = π V ( t ) ( ∀ t V , t V ∴ Π V ( G ) ⇒ ∃ t , t ∴ G and t V = π V ( t )) .Proof. With proposition 4 ("stability property of Π ") it has been shown that theprojection G V = Π V ( G ) according to the view V of a GMWf G verifying theaxioms’ visibility and the non-recursivity assumptions, is a GMWf verifying thesame assumptions. On this basis and using similar reasoning to that used to provethe proposition 5, it’s been determined that an artifact t V that is conform to G V ,is one of its target artifacts ( local target artifact for the view V ): i.e, t V ∈ arts G V .Referring to the projection process which made it possible to obtain G V , it is de-termined that the set arts G V is exclusively made up of the projections of the set arts G = { t , . . . , t n } of G ’s target artifacts. t V is therefore the projection of at leastone target artifact t i ∈ arts G of G ( t V = π V ( t i )) . Knowing that ∀ t , t ∴ G ⇔ t ∈ arts G (see proof of proposition 5), it is deduced that t i ∴ G and the proof of thisproposition is made. (cid:50) By applying the GMWf projection algorithm presented above (algorithm 2) tothe running example, one obtain the productions listed in table 2 for the differentactors respectively. In the illustrated case here, we have considered an update ofthe GMWf of the peer-review process so that it validates the axioms’ visibilityassumption.
Consider an (global) artifact under execution t , and t V = π V ( t ) its partialreplica on the site of an actor A i whose view is V . Consider the partial replica t ma j V ≥ t V obtained by developing some unlocked buds of t V as a result of A i ’scontribution. The expansion problem consists in finding an (global) artifact underexecution t f , which integrates nodes of t and t V . To solve this problem madedifficult by the fact that t and t V are conform to two different models ( G and G V = Π V ( G ) ), we perform a three-way merge [35]. We merge the artifacts t and t V using a (global) target artifact t g such that: (a) t is a prefix of t g ( t ≤ t g ) (b) t ma j V is a prefix of the partial replica of t g according to V (cid:16) t ma j V ≤ π V ( t g ) (cid:17) The proposed algorithm proceeds in two steps.18 able 2: Local GMWf productions of all the actors involved in the peer-review process.
Actor Productions of local GMWf
EC P : A G → A P : A → B (cid:35) D P : A → C (cid:35) DP : C → S (cid:35) F P : S → S (cid:107) S P : S → H (cid:35) I P : S → H (cid:35) I P : B → ε P : D → ε P : F → ε P : H → ε P : I → ε P : H → ε P : I → ε AE P : A G → A P : A → C P : C → E (cid:35) FP : E → S (cid:107) S P : S → H (cid:35) I P : S → H (cid:35) I P : H → ε P : I → ε P : H → ε P : I → ε P : F → ε P : A G → ε R P : A G → C P : C → G P : G → H (cid:35) I P : H → ε P : I → ε P : A G → ε R P : A G → C P : C → G P : G → H (cid:35) I P : H → ε P : I → ε P : A G → ε Step 1 - Search for the merging guide t g The search of a merging guide is done by (algorithm 3) generating the set oftarget artifacts denoted by G , then filtering this set to retain only those for which t is a prefix (see the definition of the prefix relationship in algorithm 3) and t ma j V is aprefix of their projection according to the view V . Step 2 - Merging t, t ma j V and t g The problem here is to find an artifact t f that includes all the contributionsalready made during the workflow execution. The structure of the searched artifact t f is the same as that of t g : hence the interest to use t g as a guide. The mergingis carried out by the algorithm 4. Technically, the three artifacts t , t ma j V and t g areexplored in depth simultaneously and a specific treatment is applied according tothe configuration of the visited nodes: if the three nodes visited at a given time19 lgorithm 3 Algorithm to search a merging guide. First of all, we have to generate the set arts G = { t , . . . , t n } of target artifacts denotedby G ; Then, we must filter this set to retain only the artifacts t i admitting t as a prefix (cri-terion (a) ) and whose projections according to V ( t i V j ) admit t ma j V as a prefix (criterion (b) ). It is said that an artifact t a (whose root node is n a = X a [ t a , . . . , t a l ] ) is a prefix of agiven artifact t b (whose root node is n b = X b [ t b , . . . , t b m ] ) if and only if the root nodes n a and n b are of the same types (i.e X a = X b ) and: a. The node n a is a bud or, b. The nodes n a and n b have the same number of sub-artifacts (i.e l = m ), the sametype of scheduling for the sub-artifacts and each sub-artifact t a i of n a is a prefix of thesub-artifact t b i of n b .We obtain the set guides = (cid:8) t g , . . . , t g k (cid:9) of artifacts that can guide the merging; Finally, we randomly select an element t g from the set guides . Algorithm 4
Three-way merging algorithm.
A prefixed depth path of the three artifacts ( t , t ma j V and t g ) is made simultaneously untilthere is no longer a node to visit in t g . Let n t i (resp. n t maj V j and n t gk ) be the node locatedat the address w i (resp. w j and w k ) of t (resp. t ma j V and t g ) and currently being visited.If nodes n t i , n t maj V j and n t gk are such that ( processing ): n t maj V j is associated with a (re)structuring symbol (fig. 6(d)) then: we take a stepforward in the depth path of t ma j V and we resume processing; n t i , n t maj V j and n t gk exist and are all associated with the same symbol X (fig. 6(a) and6(b)) then: we insert n t maj V j (it is the most up-to-date node) into t f at the address w k ; if n t maj V j is a bud then we prune (delete sub-artifacts) t g at the address w k ; we take a stepforward in the depth path of the three artifacts and we resume processing. n t i , n t maj V j and n t gk exist and are respectively associated with symbols X i , X j and X k such that X k (cid:54) = X i and X k (cid:54) = X j (fig. 6(e)) then: we add n t gk in t f at address w k . This is anupstair bud; we take a step forward in the depth path of t g and we resume processing. n t i (resp. n t maj V j ) and n t gk exist and are associated with the same symbol X (fig. 6(c)and 6(f)) then: we insert n t i (resp. n t maj V j ) into t f at the address w k ; if n t i (resp. n t maj V j ) isa bud, we prune t g at the address w k ; we take a step forward in the depth path of theartifacts t (resp. t ma j V ) and t g , then we resume processing. Proposition 7.
For any update t ma j V in accordance with a GMWf G V = Π V ( G ) , ofa partial replica t V = π V ( t ) obtained by projecting (according to the view V ) anartifact t being executed in accordance with the GMWf G of a GMAWfP verifyingthe axioms’ visibility and the non-recursivity assumptions, there is at least onetarget artifact (the three-way merge guide) t g ∈ arts G of G such as: (a) t is a prefix of t g (t ≤ t g ) (b) t ma j V is a prefix of the partial replica of t g according to V (cid:16) t ma j V ≤ π V ( t g ) (cid:17) Proof.
Thanks to the proposals 4, 5 and the artifact editing model used here ,it is established that since the artifact t being executed in accordance with G isa prefix of a non-empty set of G ’s target artifacts arts (cid:48) G = (cid:110) t (cid:48) , . . . , t (cid:48) n (cid:111) ( ∀ ≤ i ≤ n , t ≤ t (cid:48) i ), its projection t V according to the view V is a prefix of a non-empty set arts (cid:48) G V = (cid:110) t (cid:48) V , . . . , t (cid:48) V m (cid:111) of G V = Π V ( G ) ’s local target artifacts for the said view( ∀ ≤ j ≤ m , t V ≤ t (cid:48) V j ): elements of arts (cid:48) G are potential merging guides candidatesthat all verify the property (a) . In addition, using the propositions 4 and 6, it isestablished that each element of arts (cid:48) G V is the projection of at least one elementof arts (cid:48) G according to the view V (1) . Given that t ma j V is obtained by developingbuds of t V in accordance with G V , it is inferred that t ma j V is a prefix of a non-empty subset arts ma j G V ⊆ arts (cid:48) G V of local target artifacts for the view V (2) . Withthe proposition 6 once again, it is determined that for each artifact t (cid:48) V j ∈ arts ma j G V ,there is at least one artifact t g j that is conform to G such as t (cid:48) V j = π V (cid:0) t g j (cid:1) : this newset arts ma j G = { t g , . . . , t g k } is made up of potential merging guides candidates thatall verify the property (b) . Results (1) and (2) show that arts ma j G and arts (cid:48) G are notdisjoint. As a consequence, the set guides = arts ma j G ∩ arts (cid:48) G of potential mergingguides that all verify both property (a) and (b) is not empty. (cid:50) Corollary 8.
For an artifact t being executed in accordance with a GMWf G ofa GMAWfP verifying the axioms’ visibility and the non-recursivity assumptions, An artifact is developed at the level of its leaves using the productions of the GMWf to which itconforms. igure 6: Some particular cases to be managed during the expansion. nd an update t ma j V ≥ t V of its partial replica t V = π V ( t ) according to the view V , the expansion of t ma j V contains at least one artifact and the expansion-pruningalgorithm presented here returns one and only one artifact. This result (corollary 8) derives from the proof of the proposition 7 ( there isalways at least one artifact in the expansion of t ma j V under the conditions of corol-lary 8 ) and from the fact that in the last instruction of the algorithm 3, an artifact israndomly selected an returned from a non-empty set of potential guides ( only oneof the expansion artifacts is used in the three-way merging ). You can find types and functions (coded in Haskell ) that perform the pro-jections as described in this paper in the following Git repository: https://github.com/MegaMaxim10/GMAWfP-Projection-Algorithms . These tools havebeen proposed as a proof of concepts. More specifically, they include types for en-coding annotations (sequential, parallel, locked, unlocked, etc.) on artifacts, theirnodes and productions. There are also simple types for manipulating productions,artifacts, GMWf,... as well as the actual projection functions. All of these tools areprovided in a file that can be directly interpreted using a Haskell interpreter like theGlasgow Haskell Compiler . A readme and comments have been added to make iteasier to get to grips with the provided implementation as shown in the screenshotin figure 7.One observation that can be quickly made by consulting the provided Haskellcode is that, it is quite long. This shows that the proposed algorithms are difficult topresent with common notations (in pseudo-code form or even directly in code); thisis why we have opted to present them with instructions written in natural languageand sprinkled with a few mathematical formulas (it was more concise and precisethat way). Nevertheless, we have chosen to use Haskell (a functional language) tocode our functions because, the Haskell code is generally self-descriptive (i.e. veryclose to semi-formal descriptions) and more compact than those written in otherlanguages.
4. Related Works and Discussion
Some works of the literature have focused on the projection of trees that con-form to grammatical models in a cooperative editing workflow. We present some Haskell: , visited the 01/08/2020. Git: https://git-scm.com/ , visited the 01/08/2020. The Glasgow Haskell Compiler: , visited the 01/08/2020. igure 7: A screenshot of the provided Git repository. of them here and discuss our results as we go along.In their structured cooperative editing model, Badouel et al. [14] proposed atree projection algorithm operating in the general case: i.e. even in the case inwhich trees are not annotated and their roots may be invisible; the projection maythus produce a forest. The artifact projection algorithm proposed in this manuscriptis a specialization of their own in the case of annotated trees, constructed usingonly two types of productions: it was therefore necessary to be able to add new(re)structuring symbols during the projection in order to guarantee the stability ofmodels through this operation. Moreover, the scope of application of the algorithmwe propose requires that the projection always provides a single artifact: hence theaxioms’ visibility assumption.The authors of [14] also proposed a solution to the expansion problem. Moreprecisely, they proposed to associate to the updated partial replica whose expansionis sought, a tree automaton with exit states [18] generating the documents of theexpansion. This tree automaton is constructed using the global grammatical model,the considered view and the updated partial replica. In our case, an additional pa-rameter has been added: the global artifact whose partial replica has been updated.This is where the interest of performing a three-way merge comes from. Moreover,we did not need the automaton structure because we made the assumption of non-recursivity of the manipulated grammatical model. Let us also mention that ourexpansion is followed by a pruning to better correspond to the field of applicationof this paper (the decentralized execution of GMAWfP).About our expansion-pruning algorithm, note that the choice of the mergingguide is made randomly from a set of potential candidates. This considerationwas made to simplify the work presented here. Indeed, if the initial grammatical24odel is specified without ambiguity (an ambiguity could come from an executionscenario that contains another one) then there is no problem with this considera-tion. However, in the presence of a grammatical model subject to design errors,the choice of a three-way merge guide must be made with caution because it deter-mines the continuation of the execution (the scenario to follow): this choice couldtherefore be made by one of the actors involved in the execution of the process(maybe the process owner). This opens an interesting perspective on the verifica-tion of the specifications produced with LSAWfP.The authors of [16] have proposed a grammatical model for structured cooper-ative editing. They also proposed an algorithm for projecting a grammar accord-ing to a view. Their algorithm proceeds by successive rewrites of the productionswhose right hand side contains invisible symbols: the invisible symbols are re-placed by the right hand sides of productions for which they appear on the lefthand side. The rewrites are made until there are no more invisible symbols. Asin our case, (re)structuring symbols are added if necessary and the initial modelmust not admit recursion: it therefore seems that the projection of grammaticalmodels admitting recursive symbols is an interesting avenue of research. How-ever, our GMWf projection algorithm is completely based on the artifact projec-tion algorithm. Rewritings of the productions are thus implicitly realized duringthe projection of the artifacts.In a more general perspective, Foster et al. [36, 37] proposed a solution to theview update problem in the case of tree-structured data. More specifically, theyoffer a domain-specific programming language in which all expressions denotebi-directional transformations on trees. In a sense, these transformations make itpossible to project a so-called "concrete tree" in order to obtain a simplified view(a so-called "abstract view") of it. In the other direction, transformation operationsallow to merge a modified abstract view with the original concrete tree to obtaina modified concrete tree. The algorithms proposed by Foster et al. manipulateunranked trees (i.e trees with unranked nodes) while ours only manipulate rankedtrees. They are therefore not interested by documents models (grammars) whichare an essential tools in our study. Let’s note also that, the concept of views they usein their work is different from ours; it’s rather more close to the one encounteredin works on databases [38, 39, 40, 41, 42]. We are not aware of many studies that have looked at the consistency of viewsin the decentralized execution of processes using BPM technology. We herebypresent a few that have mentioned the concept of views.The studies in [43, 44, 45, 46, 47, 48, 49] propose mechanisms for the construc-tion of views guaranteeing the stability of the base models. Here, the views are in25act, process models that guarantee a certain degree of confidentiality. The studiesin [43, 44, 45, 46] apply in the case of process-centric workflows, while those in[47, 48, 49] apply in the case of artifact-centric workflows. The main difference be-tween these studies and ours is that, we manipulate trees and grammatical modelswhere they are interested in arbitrary graphs or stack automata.In the SwinDeW [50] approach to decentralised workflow management, theauthors propose a "know what you should know" policy to manage confidentiality.According to this policy, a workflow is partitioned (projected) into individual tasksafter it is modelled completely (using any workflow language), and definition ofindividual tasks is then distributed to appropriate peers for storage. Unlike ours,the SwinDeW approach is not artifact-centric and the authors do not really proposeprojection algorithms; rather, they propose a formalism for modelling each task inorder to facilitate their distribution and decentralized execution.Hull et al. [29] proposed a new approach to interoperation of organizationshubs based on business artifacts. It provides a centralized point where stakeholderscan access data of common interest and check the current status of an aggregateprocess. They proposed three kinds of access restrictions namely windows , views and Create-Read-Update-Delete (CRUD) . "Windows" provide a mechanism to re-strict which artifacts a stakeholder can see; "views" provide a mechanism to restrictwhat parts of an artifact a stakeholder can see; and the CRUD is used to restrict theways that stakeholders can read and modify artifacts. This approach differs fromours by the fact that it is centralized and that its confidentiality policy is only inter-ested in the artifacts and not in their models.
5. Conclusion
In this work, we have presented the LSAWfP language for the specification ofadministrative workflow processes using grammatical models. We then presented adecentralized and artifact-centric execution model (
P2P-WfMS-View ) of the work-flow processes specified using LSAWfP. Based on the principles of this model, weproposed versions of its key algorithms ( algorithm for projecting an artifact , algo-rithm for projecting a GMWf and algorithm for expanding a partial replica ). Theproposed algorithms are perfectly usable since we have proven the stability of ourmain mathematical tools when using them. We have implemented them in Haskelland tested them with very satisfactory results. However, in order for our algorithmsto produce the expected results, we have made some assumptions. Notably the non-recursivity of GMWf assumption, which had the direct effect of limiting a littlebit the expressiveness of LSAWfP. An interesting perspective of this work there-fore consists in proposing other versions of the algorithms presented here, which26ould take up the same fundamental principles while raising the non-recursivity ofGMWf assumption in order to offer more facility to the designers of GMAWfP. References [1] Scott McCready. There is more than one Kind of Workflow Software.
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