Interaction Expressions A Powerful Formalism for Describing Inter-Workflow Dependencies

Transcription

1 Interaction Exressions A Powerful Formalism for Describing Inter-Workflow Deendencies Christian Heinlein, Peter Dadam Det. Databases and Information Systems University of Ulm, Germany {heinlein,dadam}@informatik.uni-ulm.de Abstract Current workflow management technology does not rovide adequate means for describing and imlementing workflow ensembles, i. e., dynamically evolving collections of more or less indeendent workflows which have to synchronize only now and then. Interaction exressions are roosed as a simle yet owerful formalism to remedy this shortcoming. Besides oerators for sequential comosition, iteration, and selection, which are well-known from regular exressions, they rovide arallel comosition and iteration, conjunction, and several advanced features like arametric exressions, multiliers, and quantifiers. The aer introduces interaction exressions semi-formally, gives examles of their tyical use, and describes their imlementation and integration with state-ofthe-art workflow technology. Major design rinciles, such as orthogonality and imlicit and redictive choice, are discussed and comared with several related aroaches. 1. Introduction Everyone of us is familiar with hrases like the following frequently found in enveloes from insurance comanies or authorities: Our aologies if you receive multile letters from us today. The cost for merging them, however, would be higher than the additional ostage. In-atients of hositals might be familiar with even more unleasant haenings: The nurse comes again to take blood because another test has been ordered; examinations have to be reeated because they hav e been erformed in an incomatible order; an aointment has to be cancelled because the temorary nurse forgot to kee the atient sober, and so on. The reason for this trouble is the same in both scenarios: Work rocesses run concurrently and indeendently desite the fact that they are actually interdeendent. Even if the individual rocesses (or workflows ) are controlled by a workflow management system (WfMS), there remains a lack of inter-workflow coordination which is not addressed by current workflow technology. When trying to solve these coordination roblems with state-of-the-art aroaches, it turns out that the language constructs tyically rovided by workflow descrition languages (such as sequence, branch, and loo) are not adequate to describe workflow ensembles, i. e., dynamically evolving collections of more or less loosely couled workflows. Taking as an examle the different examinations of a atient during an inatient treatment, it is sensible to model each of them as a searate workflow because it is a self-contained, comrehensible and frequently recurring rocess by itself. If several such workflows (for the same atient) run in 1

2 arallel, most of their activities (or stes ) are still indeendent of each other and thus can be executed by themselves, but some of them must be coordinated across workflow boundaries. For an ad-hoc solution of this roblem, all affected workflows might be augmented with exlicit coordination stes, comarable to semahor oerations in arallel rogramming. It is well-known from that domain, however, that such an entanglement of alication and synchronization matters leads to very unwieldy and error-rone solutions in ractice. Therefore, it is desirable to re-aly a basic rincile of workflow management, viz the searation of the control and data flow descrition from the individual alication modules, one level higher: to searate the secification of interworkflow deendencies from the individual workflow descritions. However, since usually neither the number nor the actual tyes of the workflows articiating in an ensemble are known in advance, exlicit descritions like Activity A of workflow W 1 must follow activity B of workflow W 2 or IfA has been executed then... else... will lead to an unmanageable number of cases. In order to describe the coordination requirements in a comact and elegant means, a more imlicit and generic formalism is needed which allows a whole range of ossibilities to be described by a single exression or statement. Regular exressions are a well-known and roven instance of such a formalism from the area of comiler construction. Substituting actions or activities for inut characters or tokens, they can be emloyed to describe ermissible (or imermissible) sequences of executions. Augmenting them with oerators for exressing concurrent executions (together with some more advanced features) directly leads to interaction exressions as a concetually simle yet owerful formalism for describing inter-workflow deendencies. Desite their concetual simlicity, interaction (or even regular) exressions tend to become incomrehensible quite quickly when alied to real-world roblems. Therefore, a more user-friendly (e. g., grahical or verbal-roositional) notation is needed in order to imrove their readability, esecially for comuter science laymans such as workflow designers. The actual aearance of such a notation is irrelevant for and beyond the scoe of this aer, but it should be ket in mind throughout the following sections that an actual user will not be burdened with the mathematical formalism resented here. Section 2 commences by introducing actions and activities and the six basic oerators of interaction exressions. It roceeds with describing more advanced features, such as multiliers and quantifiers, and demonstrates their use with several examles. It concludes with some remarks about the imlementation of interaction exressions by means of an interaction manager. Section 3 uses the examle of inatient examinations to exlain the secification of inter-workflow deendencies with interaction exressions. Furthermore, it describes the ossibilities for integrating the interaction manager with current workflow technology in order to actually enforce secified constraints. Section 4 comares interaction exressions with several related aroaches, while section 5 concludes with some remarks about current and future work. 2. Interaction Exressions 2.1 Actions and Activities Activities (or stes ) are the basic building blocks of workflow descritions whose execution is requested by an external (not necessarily human) user. In order to describe inter-workflow deendencies with interaction exressions, it seems reasonable, therefore, to base them on activities, too. It turns out, however, that things become concetually easier if interaction exressions are based on actions instead, whose executions are assumed to be instantaneous ev ents (i. e., to take no time) which cannot overla in time. This does not restrict generality, since it is always ossible to describe an acitivity A (having a ositive duration in time) by a sequential comosition (see section 2.2) of two 2

3 actions, A start and A term, reresenting its start and termination, resectively. By that means it is ossible to formally reduce a concurrent execution of activities to a sequential execution of actions which can be catured with formal (e. g., language-theoretic) methods much easier. 2.2 Basic Exressions Interaction exressions (or simly exressions) are used to describe ermissible sequences of action executions. An exression itself is executed by executing a sequence of actions ermitted by the exression. If several such sequences exist (which is common), we assume as a mental model that the exression always chooses the right one, i. e., the sequence the external user has in mind. For a real imlementation this means, of course, that it must consider all ossible alternatives in order to finally accet the user s sequence if it is ermissible. In the following, interaction exressions are defined according to this simle, intuitive model. A more recise definition, based on formal language theory, is ossible, but beyond the scoe of this aer. An atomic exression a is executed by executing the action a. A selection or disjunction x y is executed by executing one of the exressions x or y. A sequential comosition x y is executed by first executing exression x and afterwards executing exression y. A sequential iteration x * is executed by sequentially executing exression x an arbitrary number of times. This is equivalent to the exression λ x x x x x x..., where λ reresents an emty sequence of actions. A arallel comosition x + y is executed by executing the exressions x and y concurrently, i. e., by arbitrarily interleaving their executions. A arallel iteration x # is executed by executing an arbitrary number of exressions x in arallel. In analogy to the sequential iteration, this is equivalent to the exression λ x x + x x + x + x... A (strict) conjunction x && y is executed by executing a sequence of actions ermitted by both exressions, x and y. In ractice, this means that actions x 1, x 2,... (y 1, y 2,..., resectively) which occur only in exression x (y) but not in exression y (x) will never be ermitted by the conjunction x && y. Since this would severely restrict the ractical alicability of the conjunction oerator, a weaker definition is used in the following which makes sure that an action occuring in one branch only is always ermitted by the other branch. Formally, this weak conjunction can be defined as follows: x & y = (x + y 1 * + y 2 * +...) && (y + x 1 * + x 2 * +...). As a simle examle, the exression (a b) & (a c) is equivalent to ((a b) + c *) && ((a c) + b *) whose first (second, res.) branch ermits the sequence ab (ac) with arbitrary interleavings of c s (b s). Therefore, the comlete exression ermits the sequences abc and ac b corresonding to the intuitive meaning of (a b) & (a c) which simly says that a has to be executed before b and before c. Weak conjunction is similar, but different from arallel comosition: If the alhabets (i. e., action sets) of the exressions x and y are disjoint, the exressions x & y and x + y are equivalent, i. e., x and y can be executed indeendently. Otherwise, their execution must be synchronised at every common action. In order to make comlex exressions involving different oerators unambiguous, the following recedence rules are defined. The unary oerators * and # have highest recedence, followed, in decreasing order, by the binary oerators, +,, and & (&& is not used in ractice and is only needed to define &). Since both unary oerators are alied ostfix and all binary oerators are associative, no rules for imlicit bracketing are necessary. Parenthesis can be used, of course, for exlicit grouing or imroving readability. 3

4 2.3 Multiliers Multiliers are a straight-forward extension of binary oerators, similar to the mathematical sum and roduct oerators, Σ and Π. is one of the oerators, +,, or &, the following definitions shall hold: x x (n times x) for n >0; x k = x n for arbitrary integers m, n. k=m x = λ for n 0; In the first line, n is called factor, while m and n are called lower res. uer bound in the second line. k is called index and can be used as a factor or bound of nested multiliers in the exression x k. As a simle examle, the exression k x states that x must be executed (sequentially) exactly k times, while n x allows m to n reetitions of x. k k=m Formally, multiliers are just syntactic sugar: they can always be relaced by ordinary binary oerators according to their definition. However, multiliers can hel to significantly reduce the size and, simultaneously, imrove the readability of comlex exressions. Furthermore, an imlementation of interaction exressions might be able to rocess a multilier exression more efficiently than its unfolded counterart. Finally, multiliers can be generalized to quantifiers (see section 2.6) which can no longer be directly reduced to the original binary oerators. 2.4 Imlicit and Predictive Choice The oerators for sequential comosition, selection, and sequential iteration resemble well-known constructs of rogramming or workflow descrition languages: sequence, branch, and loo. There is a fundamental difference, however: there are no exlicit conditions in interaction exressions. Given a selection a b, for instance, no Boolean exression is used to decide which branch to follow, but simly the fact which action is executed first. The same holds for the termination of an iteration like a *: The iteration continues as long as instances of a are executed. As soon as a ermissible subsequent action ist executed (e. g., b in the exression a * b), the iteration terminates. We call this olicy imlicit choice. Some of these decisions cannot be made immediately, howev er. Giv en an exression like a b a c, for examle, and executing action a, it is not clear which branch of the selection to choose. Therefore, the decision is ostoned, i. e., both b and c are ermitted next. If one of them is executed later, the decision is made retroactively. The same is true for an exression like a * a b. If an a is executed, it might corresond to the a in the iteration or to the subsequent one. The decision always lims one ste behind: if another a is executed, the revious one belonged to the iteration; if b is executed, it corresonded to the subsequent a. As already mentioned in section 2.2, one can assume as a mental model, that in analogy to nondeterministic automata the exression always makes the right decision. We call this behavior redictive choice. The combination of these two rinciles leads to exressions which are very elegant and comact comared to solutions based on exlicit conditions. 4

5 2.5 Examles In order to substantiate the statement just made, a few examles shall give an imression of the tyical use and exressiveness of interaction exressions. Activities As already mentioned in section 2.1, an activity A can be described by the sequential comosition A start A term. Since, in ractice, activities occur so frequently, the name of an activity A may always be used as an abbreviation for this sequence in interaction exressions. Producer and consumer Let activity roduce roduce an object which will then be consumed by activity consume. If the transort channel connecting them can hold only one object, the activities must be executed in alternating sequence starting with roduce: (roduce consume) *. If, on the other hand, the channel s caacity is unlimited, an arbitrary number of roduce-consume sequences might be executed in arallel: (roduce consume) #. This exression ermits an arbitrary number of concurrent roducers, but guarantees that the number of active consumers never exceeds the number of comleted roducers. If, finally, the channel can hold at most n objects, the number of concurrent roduce-consume sequences must be limited to n: n + (roduce consume) *= n + ((roduce consume) *). Mutual exclusion If several activities (or comlex exressions), A, B,..., access a common resource and thus must not execute concurrently, they can be synchronized with the exression (A B...) *. Readers and writers If the common resource just mentioned is an object which can be either read or written, concurrency can be increased by distinguishing readers (activity read) from writers (activity write) and allowing several readers simultaneously: (read # write) *. Arbitrary sequence To describe in a comact form that a number of activities (or comlex exressions), A, B,..., should be executed sequentially in arbitrary order, is quite hard with tyical imerative control constructs such as sequence, branch, and loo. Using arallel comosition, it is ossible to rescribe that each activity is executed exactly once: A + B +... Combining this with the above exression for mutual exclusion, immediately yields the desired behavior: (A + B +...) & (A B...) *. To secify that only m of the activities should be executed, the first art of the exression is relaced by (A? + B? +...) where x? is an abbreviation for x λ. This guarantees that each activity is executed at most once. To exress that exactly m activities should be executed, the indefinite iteration 5

6 of the second art is relaced by m (A B...), yielding the exression (A? + B? +...) & m (A B...). If, finally, m 1 to m 2 activities should be executed, the following exression might be used: (A? + B? +...) & m 2 m=m 1 m (A B...). 2.6 Parameters and Quantifiers In ractical alications of, e. g., the readers and writers roblem, there is, of course, not only one, but a large (usually unknown) number of objects on which access has to be synchronized indeendently. Therefore, it is reasonable to augment the activities read and write with a arameter, say o, reresenting the object to be accessed. Then, for every instance of the arameter o, a searate instance of the exression (read(o) # write(o)) * is needed. This can be secified as follows, using an intuitive generalisation of the multilier concet: + (read(o) # write(o)) *. o By leaving the range of the arameter o unsecified, it is indicated that this range is usually neither known exactly nor of articular interest here. Virtually, an exression + x() might be imagined as a arallel comosition with an infinite number of comonents: + x() = + x( i ), i=1 where { 1, 2,...} reresents the set of all ossible values of the arameter. (Since arallel comosition is commutative and associative, the ordering of the i is irrelevant.) Practically, this means that the exression + x() will create on demand a new instance of the subexression x() for every new value of the arameter. Similarly, it is ossible to define infinite selections as x() = x( i ). i=1 Due to their concetual similarity to the universal and existential quantifiers known from redicate logic, + and are called quantifiers, too. Desite the fact that arametric exressions and quantifiers are of essential imortance in ractice, sace does not ermit to treat them in more detail here nor to give more formal and sound definitions of them. The same is true for additional features of interaction exressions like substitution (an action can be declared as a substitute for one or more other actions), exlicit conditions (if the rincile of imlicit choice is not aroriate or sufficient for a articular alication), and temoral asects (conditions whose truth value changes with time). 2.7 Interaction Manager Interaction exressions can be imlemented by an interaction manager as follows. First, an exression x is transformed to a grah-based internal reresentation G(x), similar to [34]. Based on this grah, a notion of state is defined: An atomic state corresonds to a node of the grah and indicates that the action contained in that node is currently ermissible. A roduct state, which is introduced to deal with concurrency, is a tule of atomic states indicating that all corresonding actions are currently ermissible. Finally, a sum state, which is necessary to deal with 6

7 nondeterminism and to imlement the rincile of redictive choice, is a set of roduct states indicating that one of these roduct states is the right one corresonding to the external user s intention. Given an exression x, the interaction manager maintains a current (sum) state S(x) and a set of ermissible actions, P(x), consisting of all actions contained in the nodes of S(x). As a simle examle, the exression x = (a b c d) + (e f ) is transformed to the grah of figure 1. Its initial state is S(x) = {(a, e), (c, e)}, and thus the set of ermissible actions is P(x) = { a, c, e }. If an action of P(x) is executed by a user, e. g., a, a new state is determined according to a state transition function derived from the grah (details are beyond the scoe of this aer) leading to a new set of ermissible actions. In the examle, the atomic state a is relaced by its successor b (and consequently, (a, e) is relaced by (b, e)), while the atomic state c (and consequently (c, e)) is discarded because this alternative has roven false. Therefore, the new sum state becomes S(x) = {(b, e)}, and consequently P(x) = { b, e }. If more than one exression is given to the interaction manager, an action a should be ermissible if and only if it is ermitted by all exressions containing a. Formally, this is achieved by combining the exressions to a single exression using (weak) conjunction. In ractice, however, it is easier to maintain a searate grah, state, and set of ermissible actions for every exression, esecially if exressions shall be added and removed dynamically. The rincile of redictive choice which forces the interaction manager to ursue all ossible interretations of an action execution, might lead to intractable state exlosions when imlemented naively. In order to surmount this roblem, it is necessary to introduce an equivalence relation over roduct states which is able to reduce otherwise exonentially large sets of equivalent roduct states to a single reresentative. By that means, it becomes ossible to rocess even comlex exressions quite efficiently. Precise comlexity analyses are a toic of future work, however. Control Flow Server Even though interaction exressions are rimarily intended for describing inter-workflow deendencies, they might be used to model the behavioral asect (control flow) of individual workflows, too. In that case, the interaction manager can be used as the control flow server in a modular workflow management system architecture like MOBILE [5, 21]. Other asects, like organizational modeling or data flow, are described with other aroriate formalisms and imlemented by corresonding servers in such an architecture. 3. Inter-Workflow Deendencies 3.1 Secification To make sure that individual workflow descritions and inter-workflow deendencies will harmonize roerly, it is necessary to define a vocabulary of activities (workflow stes) in advance which serves as a common basis for both kinds of descritions. a c e b d f Figure 1: Grah-based reresentation G(x) for exression x = (a b c d) + (e f ). 7

8 For the domain of inatient examinations mentioned in the introduction, the following set of activities might be useful: order: an examination (e. g., an ultrasonograhy or an X-ray) is ordered by a ward doctor; aoint: an aointment is made with the deartment sulying the examination (e. g., internal medicine or radiology); reare: the atient is reared by a ward nurse; inform: the atient is informed by a ward doctor about otiential risks of the examination; call: the atient is called to the examination room; examine: the examination is actually erformed; reort: a reort is written (or dictated) by the examining hysician; read: the reort is read by the ward doctor. Given such a vocabulary, it is ossible, on the one hand, to use an arbitrary workflow definition language to define individual workflow tyes such as the examination workflow shown in figure 2. On the other hand, interaction exressions (res. a more user-friendly notation of them; cf. section 1) can be used to secify global constraints which are indeendent of the articular use of activities in individual workflows. For examle, if several examination workflows are erformed in arallel for the same atient, their call-examine sequences must be serialized since a atient cannot be in two examination rooms at the same time. Furthermore, it is imossible to inform or reare him for another examination while such a sequence is in rogress. (In database terms, call and examine require exclusive access to the atient.) On the other hand, it is ossible and even desirable to erform several rearations (e. g., taking blood) or informational talks simultaneously. These requirements can be summarized (for a single atient) with the following exression resembling the readers and writers roblem: ((call examine) reare # inform #) *. In analogy to this roblem, the exression should be quantified over all atients, however, in order to guarantee individual synchronization for every atient (cf. section 2.6): + ((call() examine()) reare() # inform() #) *. 3.2 Integration with Current Workflow Technology To actually enforce inter-workflow constraints like the one just shown, two general roblems have to be solved. First, the interaction manager imlementing the exressions must be able to monitor all actions erformed by the WfMS (i. e., start and termination of workflow stes) in order to adjust its state and set of ermissible actions accordingly. Second, it must be able to control which actions a user might execute (i. e., which workflow stes he might start) in order to make sure that only ermissible actions will be executed. This is esecially difficult if actions alternate between being ermissible and being not. The above exression, for examle, initially ermits to start any one of the reare order aoint call examine reort read inform Figure 2: Simle examination workflow. 8

9 stes call, reare, and inform for arbitrary atients, i. e., all of them are allowed to aear in aroriate users worklists. As soon as one of them is executed for a articular atient, however, e. g., reare( 1 ), call( 1 ) and inform( 1 ) cease to be ermissible and therefore should disaear from all worklists! Although this is very similar to the requirement that a single ste should disaear from all worklists as soon as it is executed by one user, it is not suorted for multile stes by current WfMSs. A secific solution to these general roblems deends more or less on the eculiarities of the articular WfMS. To solve the monitoring roblem, for examle, it is necessary to identify some externally observable event that takes lace whenever a ste is started or terminated by a user. If the WfMS records such events in an externally accessible database system, for examle, database triggers might be used to intercet them and to inform the interaction manager. Other systems, e. g., ProMInanD [22, 23], invoke an external rogram whenever a workflow instance is coied between the global workflow server and a user s client, and there is a one-to-one corresondence between coying of workflow instances and the execution of workflow stes: If an activity is started, the workflow instance is coied from the server to the client; if an activity is terminated, it is coied back to the server. Relacing the external coy rogram with a wraer which informs the interaction manager before executing the original coy rogram is a safe yet simle method to solve the monitoring roblem in that case. Furthermore, it is a artial solution to the controlling roblem, too, if the wraer rogram does not only inform the interaction manager about an activity to be started, but also asks whether this activity is ermissible. If it is not, the wraer might ull the emergency brake by returning an error code instead of executing the coy rogram, causing the WfMS to tell the user that the ste is currently not executable (although the actual error message might not be very instructive). Of course, this is not an ideal solution from the user s oint of view since it might haen that most of the stes aearing in his worklist are not actually executable. In order to fully solve the controlling roblem, the interaction manager must be able to temorarily remove imermissible activities from users worklists. Many WfMSs, including ProMInanD, automatically remove an activity from a user s worklist as soon as it has been started or reserved by another user. This behavior can be exloited as follows. If a articular activity A is executable from the WfMS s oint of view and therefore would aear in aroriate users worklists, but A is not ermissible from the interaction manager s oint of view, a riviliged seudo-user grabs the activity by declaring that he is willing to execute it. This causes the WfMS to remove the activity from all other user s worklists. The seudo-user does not actually execute the activity, howev er, but only waits until it becomes ermitted by the interaction manager. Then he declares to give it back to the ool of authorized users, causing the WfMS to re-insert it into the corresonding users worklists. The only rerequisite for this trick to work is to have an omniotent user having the rivilege to execute res. reserve every activity in the system. Even if the WfMS does not directly suort such a suer-user, it is usually ossible to declare a user as a temorary substitute for all other users and by that means inherit all of their rivileges. 4. Related Work Interaction exressions are, of course, not the first attemt to describe deendencies between concurrent activities. Quite similar aroaches are: regular exressions [19, 2], CoCoA ordering rules [12], life cycles [10], ath exressions [6, 7], and synchronization exressions [14, 15]. Modeling techniques, such as Petri nets [31, 29], sequence diagrams [37], and statecharts [16], also have something in common with interaction exressions. So why yet another formalism? Well, none of the alternatives just mentioned is comlete with resect to the aroach resented here. Regular exressions, in their basic form, do not rovide any constructs for exressing concurrency. The same is true for the ordering rules of CoCoA and for sequence diagrams which are just a grahical reresentation of regular exressions. Life cycles are an examle of a straight- 9

10 forward extension of regular exressions with arallel comosition. Similarly, statecharts and Petri nets rovide arallel comosition, but like almost all other aroaches, they do neither rovide arallel iteration nor conjunction, which have turned out to be quite imortant constructs in our exerience (confer the examles in section 2.5). A very limited form of arallel iteration is suorted by ath exressions, where multile instances of a simle exression (containing only selection and sequential comosition) might be executed concurrently. Parallel iteration has also been suggested for synchronization exressions [14], but discarded in the final version [15]. Synchronization exressions rovide conjunction, too, but only in its strict form which is unwieldy for ractical alications (cf. section 2.2). Desite their significance for real-world alications (cf. section 3.1), arametric exressions and quantifiers are usually not suorted by related aroaches. Path exressions are a artial excetion: Since a ath exression is art of an abstract data tye (or class ) definition, it is imlicitly quantified over all instances of that tye. This makes it imossible, however, to secify deendencies between methods of different classes. CoCoA ordering rules allow for arametric actions and rovide a forall oerator corresonding to our + quantifier. Many aroaches lack orthogonality, mostly to be easily imlementable. Path exressions, for examle, forbid nested iterations, while synchronization exressions do not allow the same action to occur in both branches of a arallel comosition, inhibiting our simle interretation of arallel iteration as x #=λ x x + x... Even though restrictions like these might seem reasonable at first glance ( Who will need such comlicated exressions? ) and may simlify an imlementation of the formalism, they should be avoided whenever ossible, because they will generally imede the develoment of exressions ( Is this combination of oerators allowed? ) and esecially obstruct the modular comosition of comlex exressions from indeendently develoed subexressions. Besides these ractically oriented aroaches, there is a variety of related theoretical aroaches, too: trace theory [1, 27], rocess algebra [4, 17], CSP [18], CCS [28], and maybe others. While these formalisms are well-suited for secifying, studying, and verifying roerties of concurrent systems, their ractical alicability to our roblem domain is limited. Usually, they do not rovide exlicit iteration oerators, but emloy recursion equations for that urose. While this is quite elegant from a mathematical oint of view, we refer closed and self-contained exressions for ractical alications. Workflow descrition languages usually rovide only standard imerative control constructs, such as sequence, branch, loo, and ossibly concurrency, which are too exlicit and inflexible for modelling workflow ensembles, i. e., dynamically evolving collections of more or less indeendent workflows which have to synchronize only now and then (cf. sections 1 and 2.4). The same holds for most advanced transaction models [11, 20], such as ConTracts [35] or FlexTransactions [25, 26], whose emhasis and strength lie in different areas, such as reliability, (forward) recovery, etc. of indivudal workflows. These asects are considered orthogonal to inter-workflow deendencies. An aroach that goes in line with ours is resented in [30]. However, since only regular exressions are allowed there to describe ermissible or imermissible interleavings of subtransactions, the exressive ower is quite limited. Klein [24] has roosed two rimitives to describe inter-task deendencies [3, 33]: order deendency and existence deendency. Similar to interaction exressions, it is ossible to describe a whole range of ermissible event sequences (corresonding to action sequences in our terminology) with a single exression based on these rimitives. When comaring the exressiveness of the two aroaches, it can be noticed that every Klein exression can be transformed to an equivalent interaction exression in rincile (in the worst case by enumerating all ermissible sequences, which is not very elegant, of course), but interaction exressions involving iteration cannot be exressed with the Klein rimitives. Some WfMSs rovide an event mechanism [32, 36] which can be emloyed to synchronize activities across workflow boundaries, similar to the idea of coordination stes mentioned in section 1. While concets like these might hel to imlement inter-workflow deendencies at run time, they aear to 10

11 be too rimitive and restricted to be useful for describing them at build time. Furthermore, they are not able to fully solve the controlling roblem mentioned in section 3.2, since events can only be used to enable ermissible activities, but not to disable (i. e., remove from worklists) imermissible ones. An aroach which is directly concerned with interacting workflows is resented in [9]. The interworkflow deendencies identified there, are quite similar to ours. A condition-action deendency, { A 1, A 2,...} < ca B, for examle, corresonds to the interaction exression (A 1 A 2...) B. The concet of workflow integration, howev er, is roosed only as a concetual device heling to build an integrated frame in which interactions can be better understood. Furthermore, it seems that only interactions between cooerating workflows are studied, whereas interaction exressions can deal with cometing workflows equally well. 5. Summary and Outlook Using the examle of interrelated medical examinations as a reresentative, we hav e shown that interworkflow deendencies cannot be ignored for ractical alications. Since neither ad-hoc solutions like exlicit coordination stes nor hard-wired secifications like if-then-else statements are really satisfactory in ractice, we have introduced interaction exressions as a simle yet owerful formalism for describing inter-workflow deendencies in an adequate way. With only a few basic building blocks sequential and arallel comosition, the corresonding iterations, Boolean oerators, and their generalisation to multiliers and quantifiers it is ossible to solve a broad sectrum of synchronization roblems. The rinciles of imlicit and redictive choice allow for very comact and elegant exressions comared to solutions based on more exlicit constructs. A rototyical imlementation of interaction exressions by means of an interaction manager as well as an interface to the WfMS ProMInanD have been built as a feasibility study. As already mentioned in section 2.7, the imlementation erforms reasonably well even for comlex exressions, but no detailed analyses of its worst-case comlexity have been carried out so far. In order to emhasize their ractical usefulness, interaction exressions have been introduced rather informally. A theoretically founded definition based on formal languages is currently under construction and shall be comleted in the near future. Based on the formal semantics, it is ossible to develo a calculus which can be used to otimize exressions, i. e., transform an exression to an equivalent one which can be imlemented more efficiently, and to recognize and eliminate malignant exressions (e. g., a * # which can be relaced by a #) causing the current imlementation to loo infinitely. (This is a well-known roblem with simle regular exressions, too [34].) In order to make comlex exressions more comrehensible, esecially for comuter science laymans, a first draft of a grahical reresentation of interaction exressions is under rearation. Furthermore, an abstraction mechanism is being develoed, which allows arbitrary subexressions to be relaced either by (arametric) macros or by user-defined (unary, binary, or n-ary) oerators. By that means, it is ossible for an exert to redefine a set of alication-secific macros and oerators which can afterwards be used by a layman without understanding their ossibly comlicated internal structure. This work will be continued in order to make interaction exressions really suitable for workflow designers. Currently, interaction exressions solve only one half of the inter-workflow coordination roblem, viz synchronization. The other half, inter-workflow communication, has not been addressed so far. It has to be exlored whether it is more reasonable to extend interaction exressions to incororate that asect or to develo an indeendent formalism. In any case, the remarks about exlicit vs. imlict araoches aly analogously: Tyical exlicit aroaches, such as message assing, will not be adequate to deal with dynamically evolving workflow ensembles. More imlicit and flexible aroaches like, e. g., generative communication [8, 13], seem to be more romising here. 11

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