write short report read short report Figure 1: Medical examination workflows

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1 Workflow and Process Snchronization with Interaction Eressions and Grahs Christian Heinlein Det. Databases and Information Sstems Universit of Ulm, German Abstract Current workflow management technolog does not rovide adequate means for inter-workflow coordination as concurrentl eecuting workflows are considered comletel indeendent. While this simlified view might suffice for one alication domain or the other, there are man real-world alication scenarios where workflows though indeendentl modeled in order to remain comrehensible and manageable are semanticall interrelated. As ragmatical aroaches, like merging interdeendent workflows or inter-workflow message assing, do not satisfactoril solve the inter-workflow coordination roblem, interaction eressions and grahs are roosed as a simle et owerful formalism for the secification and imlementation of snchronization conditions in general and inter-workflow deendencies in articular. In addition to a grah-based semi-formal interretation of the formalism, a recise formal semantics, an equivalent oerational semantics, an efficient imlementation of the latter, and detailed comleit analses have been develoed allowing the formalism to be actuall alied to solve real-world roblems like inter-workflow coordination. 1. Introduction Inter-Workflow Deendencies Current workflow management sstems (WfMS), whether commercial roducts or research rototes, do not rovide adequate means for inter-workflow coordination as concurrentl eecuting workflows are considered comletel indeendent. While this simlified view might suffice for one alication domain or the other, there are man real-world alication scenarios where workflows though indeendentl modeled in order to remain comrehensible and manageable are semanticall interrelated. As a simle eamle from the domain of medicine, consider the eamination workflows deicted in Fig. 1 describing the erformance of an ultrasonograh (left) and an endosco (right) including necessar re- and ostrocessing stes like scheduling, reort writing, etc. As long as these workflows refer to different atients, the might well be eecuted indeendentl. If the same atient is involved, however, the activities reare, inform, call, and erform 1 must be snchronized somehow as the access a limited resource, viz the atient under consideration. If for eamle, the activities order, schedule, reare, and inform of both workflows have alread been erformed, the activities call are to be eecuted net, i. e., the will be inserted into the worklists of aroriate users e. g., medical assistents of the ultrasonograh and endosco deartments, resectivel b the WfMS. As soon as one of these activities is actuall eecuted, however, the other one should temoraril disaear from the worklists or at least become marked as currentl not eecutable as a atient cannot be called to a second eamination as long as he asses through the first one. Onl after comletion of the first eamination (activit erform of the corresonding workflow), activit call of the second workflow should become eecutable again, i. e., reaear in aroriate worklists. 1 For the sake of simlicit, onl the verb of an activit (e. g., reare instead of reare atient) is used throughout the following tet. 1

2 ultrasonograh order eamination endosco order eamination schedule eamination schedule eamination reare atient inform atient reare atient call atient call atient erform eamination erform eamination write reort write short reort write detailed reort read reort read short reort write detailed reort Figure 1: Medical eamination workflows Imractical Solutions As current WfMSs neither rovide adequate means to describe nor to imlement such inter-workflow deendencies, one might resort to rather ragmatical aroaches like merging interdeendent workflows into a single workflow to transform inter-workflow deendencies to ordinar intra-workflow control flows. As soon as not onl two, but mabe fiv e, ten or twent interrelated workflows have to be merged, however, the resulting workflows will reach magnitudes which are no longer comrehensible nor manageable in ractice. Furthermore, a host of 2 n merged workflows would be necessar to cature ever ossible combination of n original workflows. Finall, tical intra-workflow control structures, like sequence, conditional and arallel branching, and ossibl loo, would force a workflow designer to rescribe a articular ordering of the eaminations ultrasonograh and endosco in the eamle above (more recisel, of the activities call and erform of the corresonding workflows) as the do not allow to describe a sequential eecution in either order. For these reasons, the idea to siml define awa inter-workflow deendencies b translating them to well-known intra-workflow control flows has to be abandoned. Another aarentl attractive idea uses inter-workflow messaging or event services rovided b some WfMSs to elicitl snchronize concurrentl eecuting workflows. While this aroach avoids the creation of unmanageable mega workflows as it retains the structure of the original workflows, it does not solve the combinational elosion roblem as, in rincial, 2 n variations of each workflow are necessar describing which messages to echange with concurrent workflows deending on the cast of the actuall eecuting workflow ensemble. Similarl, the mutual eclusion roblem, i. e., describing that the eaminations can be erformed in either order, cannot be solved with this aroach as inter-workflow messages cannot be used to temoraril disable activities which have alread been enabled b the WfMS. Therefore, the idea of reducing inter-workflow deendencies to bare message assing has likewise to be abandoned. A common roblem of both aroaches not mentioned so far is their rincial unabilit to deal with dnamic workflow ensembles where the number and the actual articiants of a set of concurrentl eecuting workflows is not known in advance and might change with time. As currentl eecuting workflows might alwas terminate and additional workflows can be initiated b a user at an time, 2

3 however, dnamicall evolving ensembles are actuall the normal case and must thus be suorted accordingl. Etended Regular Eression Formalisms In order to find a satisfactor solution to the inter-workflow coordination roblem at all, it is absolutel necessar to strictl searate inter-workflow snchronization asects from individual workflow descritions and to use an etremel fleible and declarative formalism for their secification. In some sense, this means to real a basic rincile of workflow management, viz the searation of the overall control and data flow secification of a workflow from the imlementation of individual alication modules, one level higher: Inter-workflow snchronization asects are etracted from individual workflows and described on a searate level using a tailored and well-suited formalism. In the ast, similar aroaches have been roosed for the snchronization of arallel rograms [2, 10, 25]. Instead of directl encoding snchronization conditions using semahor oerations or the like in individual rocedure imlementations, an abstract formalism based on etended regular eressions is used to describe them searatel in a comact, legible and easil adatable manner. The basic idea with these formalisms is to interret the language of an eression, i. e., the set of words it accets, as set of ermissible eecution sequences of actions where actions corresond to the start or termination of individual rocedures. B that means, it is indeed ossible to secif snchronization conditions in a ver fleible and declarative wa. Desite the fact that man similar formalisms have been roosed over the ears (cf. Fig. 2), each of them lacks one imortant oerator or the other. B carefull analsing the overall sectrum of oerators rovided, one can identif three airs of comlementar or dual oerators: There are two basic comosition oerators, sequential and arallel comosition, two corresonding closure oerators, sequential and arallel iteration, and two Boolean oerators, disjunction and conjunction. 2 Furthermore, the concet of arametric eressions and quantifiers can be found in a restricted form in some aroaches. Aart from the fact, that none of the formalisms roosed so far is concetuall comrehensive or comlete with resect to the others, most of them do not allow oerators to be arbitraril combined, but imose considerable restrictions on their nesting. In ath eressions, for eamle, the arallel iteration oerator must not contain other arallel iterations, while oerands of a arallel comosition in snchronization eressions must have disjoint alhabets. regular eressions arameters quantifiers conjunction arallel comosition CoCoA eecution rules [9] snchronization eressions [10] arallel iteration arallel iteration ath eressions [2] ev ent and flow eressions [22, 23] arallel comosition conjunction quantifiers arameters??? Figure 2: Formalisms based on etended regular eressions Interaction Eressions and Grahs This lack of orthogonalit on the one hand and the concetual incomleteness of the formalisms on the other hand calls for the develoment of a new formalism to describe snchronization requirements 2 Note that regular eressions rovide just the first oerator of each air: sequential comosition (sequence), sequential iteration (Kleene closure), and disjunction (choice). 3

4 which is at least concetuall comlete and full orthogonal and thus can fill the hole deicted b the question marks in Fig. 2. Desite its concetual comleteness, such a formalism should also be fleibl etensible with user-defined oerators in order to be otimall useful in different alication domains. Furthermore, it should be readil comrehensible even for mathematicall ignorant ersons, which suggests the use of a grahical reresentation instead of or in addition to a formal notation. Last but not least, the roosed formalism must be efficientl imlementable in order to be racticall useful, and the imlementation should be in contrast to, e. g., Petri nets and rocess algebras comletel deterministic. In order to meet the requirements just enumerated, interaction eressions and grahs have been develoed in the author s Ph. D. thesis [11, 12] as a simle et owerful formalism for the eressionor grah-based secification and imlementation of inter-action deendencies, i. e., snchronization conditions. Interaction grahs, which constitute the grahical, user-oriented view of the formalism, are introduced in Sec. 2, while interaction eressions, their formal counterart, are treated in Sec. 3. Sections 4, 5, and 6 dealing with the oerational semantics, imlementation, and comleit of interaction eressions, resectivel, av e the wa for their ractical alication which is illustrated in Sec. 7 b describing their integration with workflow management sstems. Finall, Sec. 8 concludes the aer. 2. Interaction Grahs Eamle Figure 3 shows a tical eamle of an interaction grah secifing a generic integrit constraint for atients b describing necessar snchronization requirements for the activities reare, inform, call, and erform. As all these activities refer to a articular atient as well as a articular eamination, the ossess corresonding arameters and containing, for eamle, a social securit number identifing a atient and a smbolic value like sono or endo reresenting an eamination, resectivel. 3 The ellises containing flash smbols, which in contrast to the redefined circular oerators constitute a user-defined oerator, reresent a mutual eclusion describing that a atient might either ass through eactl one eamination (middle branch) or be reared for or informed about several eaminations simultaneousl (uer and lower branch, resectivel). The for some quantifiers... secif that their bod, i. e., the subgrah in between, must be traversed for eactl one arbitraril chosen value of the arameter, while the bod of the for all quantifier reare atient, call atient, erform eamination, inform atient, Figure 3: Integrit constraint for atients 3 In the workflows of Fig. 1, these arameters have been omitted for the sake of simlicit. The might be considered global workflow variables which are imlicitl assed to all activities of the workflow. 4

5 ... might be traversed concurrentl and indeendentl for all ossible values of the arameter. Thus, these oerators constitute generalizations of the basic either or (disjunction) and as well as (arallel comosition) branchings, resectivel, deicted in Fig. 4. Finall, the arbitraril arallel oerators... allow an arbitrar number of concurrent and indeendent traversals of their bod. 4 z z Figure 4: Basic branching oerators: either or (left) and as well as (right) User-Defined Oerators To comlete the eamle above, Fig. 5 shows a ossible definition of the mutual eclusion oerator flash as a constant reetition (sequential iteration) of an either or branching containing the mutual eclusive branches,, and z. 5 Emloing such kinds of temlates does not onl simlif the grahs containing them, but also raises their level of abstraction as a user of the flash oerator does not need to know its recise definition but onl its abstract meaning. Therefore, frequentl occurring or fairl comlicated alication-secific oerators might be redefined b an interaction grah eert and alied afterwards even b uneerienced users. z z Figure 5: Definition of the mutual eclusion oerator Modular Combination of Grahs Figure 6 shows another eamle of an interaction grah secifing a generic caacit restriction for eamination deartments b describing that for each kind of eamination (quantifier... ) three 3 3 concurrent and indeendent instances (multilier... ) of the sequence call erform might be eecuted reeatedl (sequential iteration... ). Each of these sequences might be traversed with an arbitrar atient (quantifier... ). This means effectivel, that each eamination deartment can treat at most three atients simultaneousl. 4 As a mnemonic aid, a single circle (whether small or large) eresses that one branch must be chosen, while a double circle requires both or all branches to be traversed. Finall, three circles reresent an arbitrar number of arallel traversals. 5 It is also ossible to give a more general definition where the number of branches is variable. 5

6 3 3 call erform atient eamination,, Figure 6: Caacit restriction for eamination deartments Having secified searate snchronization conditions for atients (Fig. 3) and eamination deartments (Fig. 6), a couling oerator is emloed to combine these indeendentl develoed subgrahs into a single interaction grah reresenting their semantic conjunction (cf. Fig. 7). More recisel, the combined grah ermits the eecution of a articular activit if and onl if it is ermitted b all subgrahs containing this activit. Alied to the grah of Fig. 7 this means that the eecution of call and erform is ermitted if and onl if it is ermitted b both branches of the couling oerator..., while reare and inform are ermitted as soon as the are ermitted b the uer branch. In contrast to a strict conjunction oerator (denoted... ) which ermits eecution of an activit if and onl if it is ermitted b all its branches, the more loosel couling emloed in Fig. 7 is usuall much more intuitive and useful in ractice as a subgrah should not rohibit the eecution of activities which it does not elicitl mention. This kind of oen-world assumtion there might be activities which are either unknown or irrelevant at the time a grah is develoed suorts a modular develoment of small interaction grahs describing articular asects or facets of a snchronization condition and their seamless integration into larger grahs afterwards. In contrast, formalisms roviding strict conjunction onl [10] or no elicit conjunction oerator at all [22, 23] force grah develoers to augment the individuall develoed subgrahs with auiliar branches or secial snchronization smbols before combining them to larger grahs [12]. reare atient, call atient, erform eamination, inform atient, 3 3 call erform atient eamination,, Figure 7: Couling of indeendentl develoed subgrahs 6

7 3. Interaction Eressions Formal Semantics For normal alications, the meaning of an interaction grah, i. e., its set of ermissible eecution sequences, is intuitivel derived b traversing the grah from left to right according to descritive rules and recording the visited actions. 6 Formall, such a sequence of actions is called a comlete word of the grah if the traversal is comlete, i. e., reaches the rightmost end of the grah. Otherwise, if the traversal is terminated rematurel, the resulting sequence is called a artial word. In order to recisel determine the semantics of an interaction grah, the sets Φ() and Ψ() containing the comlete and artial words of, resectivel, will be defined in the following. 7 As it is ossible ticall b misusing the couling oerator to construct grahs with dead ends, i. e., grahs ossessing artial but no comlete words, artial words cannot be siml derived as refies of comlete words but hav e to be defined searatel. In order to simlif notations, interaction eressions are introduced in the following as an equivalent formal notation of interaction grahs. Eressed the other wa round, interaction grahs are merel a grahical notation of interaction eressions just like snta charts constitute a grahical reresentation of contet-free grammars. Table 8 summarizes the definition of interaction eressions (first and second column) where and z constitute recursivel defined suberessions and a reresents an abstract action a Γ= { [a 0, a 1,...,a n ] n IN 0, a 0 Λ, a 1,...,a n Ω Π} consisting of an action name a 0 Λand zero or more arguments a 1,...,a n Ω Πwhich are either concrete values ω Ω or formal arameters Π. Here, Λ, Ω, and Π denote corresonding basic sets for which the conditions Ω Π= and Ω = shall hold. Furthermore, for each Categor Φ() Ψ() α () atomic eression a { a } Σ* {, a } Σ* { a } otion Φ() { } Ψ() α () sequential comosition z Φ() Φ(z) Ψ() Φ() Ψ(z) α () α (z) sequential iteration Φ()* Φ()* Ψ() α () arallel comosition z Φ() Φ(z) Ψ() Ψ(z) α () α (z) arallel iteration Φ()# Ψ()# α () disjunction z Φ() Φ(z) Ψ() Ψ(z) α () α (z) conjunction z Φ() Φ(z) Ψ() Ψ(z) α () α (z) snchronization z Φ() κ ()* Φ(z) κ (z)* Ψ() κ ()* Ψ(z) κ (z)* α () α (z) disjunction quantifier arallel quantifier snchr. quantifier conjunction quantifier Φ( ω ) Φ( ω ) Φ( ω ) κ ( ω )* Φ( ω ) Ψ( ω ) Ψ( ω ) Ψ( ω ) κ ( ω )* Ψ( ω ) Table 8: Formal semantics of interaction eressions α ( ω ) α ( ω ) α ( ω ) α ( ω ) 6 The rectangular nodes of an interaction grah reresent so called activities ossessing a ositive duration in time. In contrast, actions corresond to oints in time without an duration. As the eact duration of an activit A is irrelevant, it is imlicitl maed to a sequence of two actions, A S and A T, reresenting the start and termination of A, resectivel. 7 As another mnemonic aid, Φ (ronounced fi) contains final or comlete words, whereas Ψ (si) contains artial words. 7

8 eression, Tab. 8 defines its set of comlete and artial words (third and fourth column, resectivel) where brackets... are used to denote abstract words Γ* and Σ reresents the set of concrete actions, Σ = { [a 0, a 1,...,a n ] n IN 0, a 0 Λ, a 1,...,a n Ω}, whose arguments a i are all concrete values. Consequentl, a concrete word w Σ* corresonds to a sequence of concrete actions eecuted in the real world. The concatenation (UV) and Kleene closure (U*) of languages U, V Σ* is defined as usual, whereas the shuffle of words u, v Σ* and languages U, V Σ* as well as the corresonding closure is defined as follows [23, 10]: 8 u v = { u 1 v 1...u n v n n IN, u 1, v 1,...,u n, v n Σ*, u 1...u n = u, v 1...v n = v }, U V = n U i = i=1 u v = { w Σ* u U, v V : w u v }. u U v V { } ( n 1 U i ) U n i=1 for n =0, for n >0, U# = n n=0 i=1 U = u 1... u n. n IN 0 u 1,...,u n U For an eression, a arameter Π, and a value, ω denotes the eression derived from b relacing ever occurrence of the arameter with the value ω. Infinite unions and intersections are defined as usual, whereas the shuffle of infinitel man languages U ω Σ*()iseither emt or can be reduced to a union of finite shuffles if all articiants U ω contain the emt word [12]: U ω = n IN ω 1... ω n Ω n U ω i, i=1 if U ω for all, otherwise. Finall, Tab. 8 defines the alhabet α () of eressions (last column) which is needed for the definition of the alhabet comlement κ () = α () \ α (). Unfortunatel, sace does not ermit a more detailed motivation and elanation of the definitions given in this section. Proerties of Interaction Eressions Based on the definitions of Tab. 8, two interaction eressions 1 and 2 are considered equal or equivalent, if the ossess the same alhabet and accet the same comlete and artial words. 9 Given this equivalence relation, numerous useful roerties of interaction eressions, like commutativit, associativit, or idemotence of oerators, which are intuitivel evident, can be formall roven [12]. Furthermore, interaction eressions can be comared with well-known formalisms like regular eressions and contet-free grammars regarding their eressiveness. While it is obvious that interaction eressions are more eressive than regular eressions, their relation to contet-free grammars is not et eactl determined. On the one hand, there are eressions, e. g., = ( a b c) (a b c), whose language, Φ() = { a n, b n, c n n IN 0 }, is not contet-free. On the other hand, there are contet-free grammars secifing, e. g., alindromes, whose language is resumabl not eressible with interaction eressions as the deliberatel do not allow recursive eressions. As these questions are of little relevance for ractical alications of interaction eressions, the hav e not been investigated in more detail. 8 Note that, in the first definition, ui and v i do not reresent actions Σ,butsubwords Σ* consisting of zero or more actions. 9 More recisel, as 1 and 2 might contain unbound arameters, ever air of concretions ( 1 ) ω 1,...,ω k 1,..., k and ( 2 ) ω 1,...,ω k 1,..., k (for arbitrar arameters 1,..., k Πand values ω 1,...,ω k Ω) must accet the same comlete and artial words. 8

9 4. Oerational Semantics of Interaction Eressions State Model Given the formal semantics of interaction eressions, it is ossible in rincial to construct an algorithm solving the word roblem giv en an interaction eression and a concrete word w, decide whether w is a artial or comlete word of b more or less directl transforming the definitions of Ψ() and Φ() into eecutable code. The roblem with this algorithm is, however, that it is hoelessl inefficient as its comleit grows eonentiall with resect to the length of the word w ev en for ver simle eressions [24, 12]. In order to obtain a more efficient and racticall useful imlementation of interaction eressions, it is thus necessar to introduce an oerational state model comarable in some sense to finite state machines ticall used for the imlementation of regular eressions. For that urose, ever interaction eression is assigned an initial state σ () where a state might be a comle, hierarchicall structured mathematical object. Furthermore, a state transition function τ is defined which mas a state s and an action a to a successor state s = τ a (s). Finall, two state redicates, ψ (s) and ϕ(s), are introduced which corresond directl to the sets Ψ() and Φ() of the formal semantics (cf. below). The nature of these definitions allows them to be transformed to eecutable rogram code quite directl. To further imrove the efficienc of the so constructed imlementation, an equivalence relation is introduced for states based on the redicates ψ and ϕ and an otimization function ρ is defined which mas some states s to equivalent, but less comle states ŝ = ρ(s) which can be rocessed more efficientl. Intuitivel, the state model formalizes the descritive idea of traversing an interaction grah. That means, the initial state σ () of an eression describes the starting osition of a walker (or a grou of walkers) who wants to walk through the corresonding interaction grah, while a state transition τ a (s) reresents the traversal of an action a. A successor state σ w (), derived from the initial state σ () b aling a sequence of state transitions corresonding to a word w, describes the set of all ossible ositions the walker(s) might have reached after traversing the sequence of actions w. Such a state is said to be valid, which is equivalent to its redicate ψ being true, if the sequence w is ermissible, i. e., constitutes a artial word of. It is called a final state, which is equivalent to its redicate ϕ being true, if the walker(s) might have reached the end of the grah after traversing the actions of w. To actuall guarantee the correctness of the state model with resect to the formal semantics of interaction eressions, the following equivalences must hold for ever word w Σ*: w Ψ() ψ (σ w ()) = true and w Φ() ϕ(σ w ()) = true. The corresonding roof constitutes a ver large structural induction using several smaller comutational inductions (verifing roerties of the states σ w () for the different categories of eressions ) as lemmas. Furthermore, an auiliar theorem must be roven in arallel to make sure that quantifier eressions, though constituting concetuall infinite eressions, can nevertheless be imlemented using finite states [12]. Eamle As sace does not ermit to resent the definitions of the state model in full detail, a single eamle should suffice to give the reader a taste of their nature. The states of a arallel comosition = z are tules [, A] consisting of the arallel comosition oerator and a set A of alternatives describing ossible ositions of walkers in the grah corresonding to. Each alternative constitutes a air of substates [l, r], where l and r reresent states of the left and right oerands and z of the eression, resectivel, describing in turn ossible ositions of walkers in the corresonding subgrahs. The initial state of consists of a single alternative containing the initial states of the suberessions and z: 9

10 σ () = [, A] where A = { [σ (), σ (z)] }. As the branches of a arallel comosition are eecuted concurrentl and indeendentl, the traversal of an action a Σ in might be erformed in either branch, or z. That means, that a state transition τ a (s) of a state s = [, A] should relace each alternative [l, r] A with two transformed alternatives [l, r] and [l, r ] where l = τ a (l) and r = τ a (r) reresent the corresonding successor states of l and r, resectivel: τ a (s) = [, A ] where A = { [τ a (l), r] [l, r] A } { [l, τ a (r)] [l, r] A }. A state s = [, A] should be considered valid or final, if and onl if it contains an alternative [l, r] A where both substates l and r are valid or final, resectivel: ψ (s) = (ψ (l) ψ (r)), ϕ(s) = [l, r] A (ϕ(l) ϕ(r)). [l, r] A Finall, a state s = [, A] might be otimized b removing alternatives containing invalid substates as these do not reresent reasonable ositions of walkers in the grah: ρ(s) = [, Â] where  = { [l, r] A ψ (l) ψ (r) }. 5. Imlementation of Interaction Eressions Imlementation of the State Model As alread mentioned in Sec. 4, the nature of the definitions of the functions σ, τ, ψ, ϕ, and ρ allows to transform them to eecutable rogram code quite directl. It turns out, however, that the state redicate ψ is disensible if invalid states are alread recognized b the otimization function ρ and maed to a secial null state. Furthermore, as the state transition function τ and the otimization function ρ are alwas alied successivel, it makes sense to combine them into a single otimized state transition function ˆτ a (s) = ρ(τ a (s)). The remaining functions, σ (), ˆτ a (s), and ϕ(s), can be readil imlemented using an suitable rogramming language. Solution of the Word and Action Problems Assuming corresonding function imlementations init(), trans(), and final() in C++, it is easil ossible to imlement to level functions word() and action() solving the following roblems (cf. Fig. 9): 1. The function word() solves the word roblem, i. e., it decides whether a sequence w of n actions is a comlete, artial, or illegal word of an interaction eression and returns a corresonding integer value. For that urose, the initial state s of is comuted (function init()) and successivel transformed using the actions w[i] of w (function trans()). If the resulting state s is a final state (function final()), w constitutes a comlete word of ; otherwise, if s is valid (i. e., different from the null state), w is a artial word of ; otherwise, w is illegal. 2. The function action() solves the so called action roblem. After comuting the initial state s of the eression, it successivel reads actions a (function ReadNetAction()) and decides whether each such action is currentl ermissible. For that urose, a tentative state transition is erformed to check whether the successive state t is valid. If it is, a is acceted and the state transition is actuall erformed b relacing the current state s with the successor state t. Otherwise, a is rejected and the current state s remains unchanged. As will be elained in Sec. 7, solving the action roblem is highl relevant for ractical alications of interaction eressions, while the solution of the word roblem is more or less a b-roduct of rimaril theoretical interest. 10

11 // Functions imlementing the state model. State init(er ); // Return the initial state of eression. State trans(state s, Action a); // Perform an otimized state transition // of state s with action a. bool final(state s); // Determine whether s is a final state. // Function to solve the word roblem. int word(er, Action* w, int n) { State s = init(); for (int i = 0; i < n; i++) s = trans(s, w[i]); } if (final(s)) return 2; else if (s) return 1; else return 0; // Comlete word. // Partial word. // Illegal word. // Function to solve the action roblem. void action(er ) { State s = init(); while (true) { Action a = ReadNetAction(); if (State t = trans(s, a)) { rintf("accet.\n"); s = t; } else rintf("reject.\n"); } } Figure 9: Solution of the word and action roblems 6. Comleit of Interaction Eressions Desite the fact, that statements about the comutational comleit of interaction eressions are highl relevant for ractical alications, sace does not ermit to treat this toic in much detail. Nevertheless, the main results roviding the basis for a successful ractical emloment shall be briefl resented. Generall, there is a good news and a bad news about the comleit of interaction eressions. The bad news is, it is ossible to construct malignant eressions, i. e., eressions for which the comleit of a state transition (in the current imlementation) grows eonentiall with resect to the length of the action sequence rocessed so far. The good news is, those eressions do not seem to occur in ractical alications. In order to substantiate this admittedl vague statement, etensive and detailed analses about the growth and evolution of states of an eression have been carried out. For eamle, the size of a arallel comosition state s = [, A], i. e., the cardinalit of the set of alternatives A, otentiall grows b a factor of two for each state transition (cf. Sec. 4). In ractice, however, the transformed alternatives [l, r] and [l, r ] often contain invalid substates l or r causing them to get immediatel removed b the subsequentl alied otimization function ρ. Therefore, the cardinalit of A and thus the comleit of subsequent state transitions remains nearl constant for man ractical eamles. To obtain more recise roositions about the actual behaviour of eressions, several useful subclasses of interaction eressions have been identified, e. g., quasi-regular eressions, comletel and uniforml quantified eressions, etc., for which detailed criterions for their benignit have been elaborated. For eamle, it can be shown that quasi-regular eressions (i. e., eressions not containing arallel iterations or quantifiers) are harmless (the comleit of a state transition remains constant) and that comletel and uniforml quantified eressions (which constitute the normal case of quantified eressions in ractice) are benign (the comleit of a state transition grows olnomi- 11

12 all with resect to the length of the action sequence rocessed so far). Furthermore, these roositions can be used in combination to evaluate ste b ste that a given eression is benign. To ut it in a nutshell, all ractical eamles considered so far including those resented in this aer hav e been formall roven benign using the comleit roositions develoed in [12]. Furthermore, the actual degree of the olnomial growth is rarel greater than 1 or 2. On the other hand, malignant eressions including a suitable word for which the actuall behave malignant hav eto be selectivel constructed and do not seem to have an ractical relevance. 7. Integration with Workflow Management Sstems Coordination and Subscrition Protocols Having designed interaction eressions and grahs (Sec. 2), defined their formal semantics (Sec. 3), develoed, verified, and imlemented an equivalent oerational semantics (Secs. 4 and 5), and finall roved its efficienc for racticall relevant eressions (Sec. 6), the question arises how interaction eressions and grahs can actuall be emloed to snchronize the eecution of real-world activities. Assuming that these activities will be eecuted b some sort of interaction clients (ticall workflow management sstems), a central scheduler or interaction manager and a suitable coordination rotocol is needed to monitor and control the eecution of actions (cf. Fig. 10, left side). 1. ask 1. subscribe interaction client 2. rel interaction manager 2. inform interaction client 3. eecute actions reare atient, inform atient, 4. confirm interaction grah/eression call atient, 5. state transition reare atient, erform eamination, 4. unsubscribe call atient, 3. udate worklists actions erform eamination, inform atient, Figure 10: Coordination and subscrition rotocols To make sure that a client does not eecute an action which is currentl not ermitted b the given interaction grah, the client has to ask the interaction manager for ermission first (ste 1). Deending on the current state of the grah, the interaction manager relies either es or no (ste 2). If a ositive answer is received, the client actuall eecutes the resective action (ste 3) and confirms its eecution (ste 4) causing the interaction manager to erform a corresonding state transition of the grah (ste 5). Otherwise, the client must refrain from eecuting the action now and tr again later. In order to avoid bus waiting in that case causing unnecessar communication and interaction manager workload, a client can subscribe to a articular action (ste 1, right side of Fig. 10) causing the interaction manager to inform him about ever status change of the resective action (ste 2), i. e., the client receives informational messages whenever the status of a subscribed action changes from ermissible to non-ermissible or vice versa. These messages can be used on the one hand to kee 12

13 users worklists u to date (ste 3) and on the other hand to wait assivel for the right moment to ask again for ermission to eecute an action. Finall, if a client is no longer interested in the status of an action, a corresonding unsubscribe message (ste 4) tells the interaction manager to sto sending informations about this action. As sace does not ermit to discuss these rotocols in more detail, the interested reader is referred to [12], where several alternative coordination rotocols, ossessing different comleit and articular advantages and disadvantages, are resented and to avoid the interaction manager to become a bottleneck generalized to alication scenarios involving multile interaction managers. Furthermore, the emloment of ersistent message queues [1] for the communication between interaction manager and clients as well as recover strategies of the interaction manager are described. Adatation of Worklist Handlers versus Workflow Engines In order to force a WfMS, which is er se not designed to ask anbod else for ermission before eecuting an activit, to articiate in a coordination rotocol, two alternative strategies can be ursued ossessing different advantages and disadvantages. As the runtime comonent of a WfMS basicall consists of a workflow engine communicating with several worklist handlers via the WfMS s API, either the workflow engine or the individual worklist handlers can be adated to become interaction clients articiating in a coordination rotocol with an interaction manager (cf. Fig. 11). interaction manager coordination rotocol adated worklist handler... adated worklist handler standard worklist handler... standard worklist handler WfMS API WfMS API standard workflow engine adated workflow engine coordination rotocol interaction manager Figure 11: Adatation of worklist handlers (left) versus workflow engines (right) As the WfMS s API is either standardized b the Workflow Management Coalition (WfMC) or at least documented b the vendor, it is common ractice to relace the standard worklist handlers of a WfMS with customized imlementations fitting better into the overall aearance of users deskto environments or the like. Under these circumstances, it takes little etra effort to incororate a coordination rotocol into such a customized worklist handler imlementation causing it to become a central mediator between workflow engine and interaction manager (left side of Fig. 11). In this scenario, an adated worklist handler offers and eecutes onl those activities which are regularl scheduled b the 13

14 workflow engine and currentl ermitted b the interaction manager, whereas the workflow engine remains comletel unchanged and does not even know of the interaction manager s eistence. Although this solution is rather eas to realize, it has several drawbacks in ractice. First of all, as ev er worklist handler has to communicate with the interaction manager, it introduces substantial communication overhead. Secondl, as the workflow engine is not involved in the coordination rotocol, it might haen that activities will be eecuted accidentall through a standard worklist handler of the WfMS, i. e., the aroach is not comletel waterroof. A third roblem arises from the fact that worklist handlers usuall run on users deskto comuters which are rather unreliable. If, for instance, a user switches off his PC while the worklist handler erforms ste 3 of the coordination rotocol (cf. Fig. 10), the interaction manager waits in vain for the confirmation in ste 4 causing him to remain stuck in a critical region comrising stes 2 to 5. The onl wa to alleviate this roblem is to use a more comlicated coordination rotocol inducing even higher communication overhead [12]. In order to remed all these shortcomings, it is necessar to incororate the coordination rotocol directl into the workflow engine (cf. Fig. 11, right side). In that case, the adated workflow engine offers and eecutes onl those activities which are regularl scheduled according to the resective workflow definitions and currentl ermitted b the interaction manager, whereas the worklist handlers are comletel unaffected. (Of course, it is ossible to use customized imlementations anwa.) Though absolutel referable in rincial, this solution requires substantiall more design and imlementation effort as additional functionalit has to be incororated into an alread fairl comle software sstem, viz a workflow engine. Furthermore, this solution can onl be realized b the WfMS vendor ossessing the workflow engine s source code and documentation, while the adatation of worklist handlers is realizable b customers, too. 8. Conclusion Interaction eressions and grahs constitute a fleible and eressive formalism for the secification and imlementation of snchronization conditions in general and inter-workflow deendencies in articular. In addition to a declarative semi-formal interretation (traversing interaction grahs), a recise formal semantics, an equivalent oerational semantics, an efficient imlementation of the latter, and detailed comleit analses have been develoed allowing the formalism to be actuall alied to solve real-world roblems like inter-workflow coordination. In contrast to other formalisms based on etended regular eressions, interaction eressions are concetuall comrehensive and comletel orthogonal. Comared to other well-known aroaches for the secification of concurrent sstems, eseciall Petri nets [21, 16] and various kinds of rocess algebras [13, 14, 20], their behaviour is full deterministic, even though this heavil comlicates their oerational semantics and imlementation [12]. Desite the fact that inter-workflow deendencies occur frequentl in ractical alications, the have not received much attention in the workflow communit et. Neither secial issues of journals devoted to the overall toic of workflow management [5, 6, 7, 8, 17] nor books reflecting the state of the art in that field [26, 15] have reall addressed the roblem so far. The same holds for conference and worksho roceedings in general where the number of aers dealing with other workflow management roblems, e. g., fleibilit and scalabilit, is steadil increasing. Two noteable ecetions are [3] and [18]. Both aroaches, however, are not able in rincial to deal with dnamicall evolving workflow ensembles whose articiants are not known in advance and might change with time. Therefore, the thorough develoment of interaction eressions and grahs and their alication to coordinate dnamicall evolving workflow ensembles constitutes a ioneering aroach towards a general solution of the inter-workflow coordination roblem. In addition to a ver mature core imlementation of interaction eressions based on the formall verified oerational semantics (cf. Sec. 5), a snta-driven editor for interaction grahs has been develoed to facilitate their creation in ractice. Furthermore, the coordination and subscrition rotocols described in Sec. 7 have been rototicall imlemented and tested for the WfMS ProMInanD [19]. Their integration into the net generation WfMS ADEPT [4] is a toic of future work. 14

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