J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of workflow management is to handle cases as efficient and effective as possible. A workflow process is designed to handle similar cases. Cases are handled by executing tasks in a specific order. The workflow process model specifies which tasks need to be executed and in what order. Petri nets [6] constitute a good starting point for a solid theoretical foundation of workflow management. Clearly, a Petri net can be used to specify the routing of cases (workflow instances) Tasks are modeled by transitions and causal dependencies are modeled by places and arcs. As a working example we use ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....places as follows. A place is a start place if and only if it is a source place, i.e. a place without any ingoing arcs. A place p is an end place if every transition that consumes tokens from p also produces at least one token for p. Formally, a place is an end place if and only if it is a trap [6]. Note that any sink node is a trap, i.e. an end place. Any node of the extended workflow net should be on a path from some start place to some end place. Finally, we drop the assumption that every transition corresponds to some task. Transitions that do correspond to tasks are called task ....

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, 1995.

....elements are used to describe sequential, conditional, parallel and iterative routing thus specifying the appropriate route of a case [19,23] Many cases can be handled by following the same workflow process definition. As a result, the same task has to be executed for many cases. Petri nets [11] have been proposed for modeling workflow process definitions long before the term workflow management was coined and workflow management systems became readily available. Consider for example Information Control Nets, a variant of the classical Petri nets, already introduced in the late ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....P2P approach heavily depends on the inheritance notions described in [7, 14, 15] 9 2.1 Place Transition nets In this section, we define a variant of the classic Petri net model, namely labeled Place Transition nets. For a more elaborate introduction to Petri nets, the reader is referred to [21, 41, 43]. Let # be some universe of identifiers; let # be some set of action labels. # # # # # is the set of all visible labels. The role of # , the silent action, will be explained later. We assume that the reader is familiar with basic mathematical notations. We use P### to denote the powerset of ....

....stop transitions in # # implies that we can partition the transitions of # # in two subsets ## and # # such that # # # . ####### # # ### # ## , # # . because all stop transitions have been removed. Now we apply the well known exchange lemma (see for example page 23 in [21]) which allows us to project # # onto the transitions in ## and # # : # ## and # ## . Since . the exchange lemma shows that we can first execute # ## followed by # ## . Let state # ## be the state after executing # ## , i.e. ## # ## # ### ## ## # ## ## #. It is easy to see that ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....then we define a subclass of Place Transition nets tailored towards workflow modeling and analysis (i.e. WFnets [1, 3] 2.1 Petri nets We use a variant of the classic Petri net model, namely Place Transition nets. For an elaborate introduction to Petri nets, the reader is referred to [10, 22, 23]. Definition 2.1. P T nets)An Place Transition net, or simply P T net, is a tuple (P, T, F) where: 1. P is a finite set of places, 2. T is a finite set of transitions such that P T 0, and 3. F C (P x T) U (T x P) is a set of directed arcs, called the flow relation. A marked P T net is a ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

.... then there must be an arc from any input place of t to any output transition of s (see Appendix B for a formal definition of a free choice Petri net) One important characterisation of Synchronizing Workflow Models is that the Petri net representation of the join constructs is not free choice (see [DE95] for a detailed discussion of free choice Petri nets) In Section 5.4 it will be shown that some Synchronizing Workflow Models are inherently non free choice. Having informally established the semantics of Synchronizing Workflow Models, Definition 4.1.16 formally defines their syntax, while ....

....M(p) 0) In Synchronizing Workflow Model 142, if the place p or p contains a token, there is a firing sequence producing a token for either place q or (Theorem 5.4.1) If one of these places already has a token (suppose it is a true place) according to the Monotonicity Lemma (see e.g.p. 22 of [DE95]) through application of this firing sequence a second token can be produced for this place or its corresponding false place. Having established some basic properties of well behaved Standard Workflows and Synchronizing Workflows, it is possible to show that any Synchronizing net can be ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, United Kingdom, 1995.

....used in the remainder of this paper. First, we introduce standard Petri net notations, then we define the class of WF nets. 2.1 Petri nets We use a variant of the classic Petri net model, namely Place Transition nets. For an elaborate introduction to Petri nets, the reader is referred to [10, 20, 21]. Definition 2.1. P T nets) 1 An Place Transition net, or simply P T net, is a tuple (P, T, F) where: 1. P is a finite set of places, 2. T is a finite set of transitions such that P T = J, and 3. F C (P x T) U (T x P) is a set of directed arcs, called the flow relation. A marked P T net is ....

....a very pragmatic argument. If we drop any of the requirements stated in Definition 4.3, relation w does not contain enough information to successfully mine all processes in the resulting class. The reader familiar with Petri nets will observe that SWF nets belong to the class of free choice nets [10]. This allows us to use efficient analysis techniques and advanced theoretical results. For example, using these results it is possible to decide soundness in polynomial time [2] SWF nets also satisfy another interesting property. Property 4.4. Let N (P, T, F) be an SWF net. For any a, b T ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....in the context of Synchronizing Workflow Models. One True token All True tokens Figure 8: Join semantics for Synchronizing Workflow Models A free choice Petri net is a net in which the choice between two transitions competing for the same token is never influenced by the rest of the system [DE95]. On a structural level it means that a Petri net is free choice if[ for every place p and every transition t of this net: if there is an arc from a p to t, then there must be an arc from any input place of t to any output transition ofp (see Appendix A for a formal definition of a free choice ....

.... then there must be an arc from any input place of t to any output transition ofp (see Appendix A for a formal definition of a free choice Petri net) One important characterisation of Synchronizing Workflow Models is that the Petri net representation of the join constructs is not free choice (see [DE95] for a detailed discussion of free choice Petri nets) In Section 4.3 it will be shown that some Synchronizing Workflow Models are inherently non free choice. Having informally established the semantics of Synchronizing Workflow Models, Definition 2.16 formally defines their syntax, while ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, United Kingdom, 1995.

....While we will not elaborate on the precise notion chosen, it is of interest to mention that it is based on weak bisimulation and does not treat actions # and # in parallel as equivalent to a choice between ## or ##. Standard Workflow Models essentially form a subclass of Free Choice Petri nets [12]. Hence Standard Workflow Models do not support advanced forms of synchroFIT nization such as present in Pattern 7 (Synchronizing Merge) and Pattern 9 (Discriminator) which were proven to be inherently non free choice [29, 30] In addition, while Free Choice Petri nets support the concept of ....

....domain to YAWL as possible. Given the expressiveness of YAWL, these results are directly applicable to a range of existing workflow languages. For example, we expect that for restricted YAWL specifications we can use invariants comparable to place and transition invariants in Petri nets [12, 27, 39]. 6 Conclusion Through the analysis of a number of languages supported by workflow management systems a number of patterns was distilled in previous work. While all these patterns can be realised in high level Petri nets, some of these patterns can only be realised in a rather indirect way ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....of the joins is shown in the context of Synchronizing Workflow Models. One True token All True tokens Figure 8: Join semantics for Synchronizing Workflow Models A free choice Petri net is a net in which the choice between two enabled transitions is never influenced by the rest of the system [DE95]. On a structural level it means that a Petri net is free choice if[ for every place and transition of this net if there is an arc from a place p to a transition t, then there must be an arc from any input place of t to any output transition of s (see Appendix A for a formal definition of a ....

.... there must be an arc from any input place of t to any output transition of s (see Appendix A for a formal definition of a free choice Petri net) One important char acterisation of Synchronizing Workflow Models is that the Petri net representation of the join constructs is not free choice (see [DE95] for a detailed discussion of free choice Petri nets) In Section 4.3 it will be shown that some Synchronizing Workflow Models are inherently non free choice. Having informally established the semantics of Synchronizing Workflow Models, Definition 2.16 formally defines their syntax, while ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, United Kingdom, 1995.

....to verify soundness. For a complex WF net it may be intractable to decide soundness. For arbitrary WF nets liveness and boundedness are decidable but also EXPSPACE hard, cf. Cheng, Esparza and Palsberg [5] Free choice Petri nets have been studied extensively (cf. Best [3] Desel and Esparza [6], Hack [8] because they seem to be a good compromise between expressive power and analyzability (cf. Definition 8) It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem (Desel and Esparza [6] enables ....

....and Esparza [6] Hack [8] because they seem to be a good compromise between expressive power and analyzability (cf. Definition 8) It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem (Desel and Esparza [6]) enables us to formulate the following corollary. Corollary 1. The following problem can be solved in polynomial time. Given a free choice WF net, to decide if it is sound. Proof. Let ## be a free choice WF net. The short circuited net ## is also free choice. Therefore, the problem of deciding ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....P T nets. First, we introduce some basic definitions and useful properties. Second, we introduce some analysis techniques on P T nets. Readers familiar with Petri nets can browse through this section to become familiar with the notations used. An extensive treatment of Petri nets can be found in [16, 33, 34, 35]. In this section, we restrict ourselves to the material that is needed to understand the foundations of Woflan. 2.1. Basic definitions 2.1.1. P T nets A P T net is a directed graph with two kinds of nodes: transitions and places. Arcs in the graph always connect a node of one kind to a node ....

....INCOME, LEU, and MOBILE) allow arbitrary non free choice constructs. Second, for a free choice WF net, it can be decided in polynomial time whether or not the net is sound, because it is possible to verify in polynomial time whether the corresponding short circuited WF system is live and bounded [16]. Given these two facts, one could envision a verification tool that focuses on free choice WF nets. However, for Woflan, we decided differently. One of the main requirements for Woflan mentioned in the introduction is that it is workflow product independent. Allowing non free choice WF nets ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....algorithm Feasible(S) for the problem of deciding if a system of linear equations S with integer coefficients has a solution in the natural numbers. It is easy to decide if every siphon of a net N is marked at a given marking M . The following (deterministic) algorithm, due to Starke [33, 5], does it for you. It first computes the largest siphon R contained in the set of places not marked at M . Clearly, all nonempty siphons are marked at M if and only if R is empty. Algorithm All Siphons Marked(N , M ) variable: R of type set of places; begin R : set of places of N unmarked ....

....time. Among the many interesting polynomial questions for conflict free nets are all those that can be expressed in the fragment of CTL with syntax : s j : j 1 2 j EX j EF (see [7] Among the some interesting polynomial questions for live free choice nets are the following [5]: Is there a reachable marking which marks a given place Is there a reachable marking which does not mark a given place Is there a reachable marking which enables a given transition Is the initial marking reachable from every reachable marking Is there a run that does not ....

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J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

....absent in state machines) however for a large class of Petri nets (containing nearly all the nets useful for modeling work ows) there exists a systematic method of simulating them on the Bond multi plane state machine. It is convenient to introduce here the following de nitions and a theorem from [9]. Subnets. Let (S; T ; F ) be a Petri net and X S [ T . The triple (S X;T X;F [ X X) is the subnet of N generated by X . S components. Let N 0 be the subnet of a net N generated by a nonempty set X of nodes. N 0 is an S component if s [ s X for every place s of N N 0 is a ....

J. Desel and J. Esparza. Free Choice Peri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

....in several disjoint S nets, each of the S nets can be simulated on a separate Bond plane. For connected nets such partition is not possible, however, we can attempt to cover the original net with S nets. It is convenient to introduce here the following definitions and a theorem quoted from [7]. Subnets. Let (S; T ; F ) be a Petri net and X S [ T . The triple (S X;T X;F [ X Theta X) is the subnet of N generated by X . S components. Let N 0 be the subnet of a net N generated by a nonempty set X of nodes. N 0 is an S component if ffl ffls [ sffl X for every place s of N ....

J. Desel and J. Esparza. Free Choice Peri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

....P T nets. First, we introduce some basic definitions and useful properties. Second, we introduce some analysis techniques on P T nets. Readers familiar with Petri nets can browse through this section to become familiar with the notations used. An extensive treatment of Petri nets can be found in [15, 30]. 2.2 Basic definitions 2.2.1 Net structure A P T net is a directed graph with two kinds of nodes: transitions and places. Arcs in the graph always connect a node of one kind to a node of the other kind. To Figure 1: The example P T net N identify the elements in a P T net, we introduce the ....

....decide soundness. Theorem II (Free choice vs. soundness) Given a free choice WF net, it can be decided in polynomial time whether or not the net is sound. Proof Let N be a WF net. It is possible to verify in polynomial time whether the short circuited WF system (N , i ] is live and bounded [15]. Theorem III (Soundness and free choice vs. Scoverability) Let N be a sound, free choice WF net. The shortcircuited WF net N is S coverable. Proof This follows directly from Theorem I and the fact that a net which is free choice, live, and bounded must be S coverable ( 15] In the analysis ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, UK, 1995. 40

....the term confusion is often used to refer to the situation shown in Figure 5. t2 t3 i t4 t5 t1 o c1 c2 c3 c4 Figure 5: A non free choice WF net containing a mixture of parallelism and choice. Free choice Petri nets have been studied extensively (cf. Best [5] Desel and Esparza [8, 7, 10], Hack [13] because they seem to be a good compromise between expressive power and analyzability. It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well knownRank Theorem (Desel and Esparza [8] allows us to formulate the ....

....[5] Desel and Esparza [8, 7, 10] Hack [13] because they seem to be a good compromise between expressive power and analyzability. It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well knownRank Theorem (Desel and Esparza [8]) allows us to formulate the following corollary. Corollary 1 The following problem can be solved in polynomial time. Given a free choice WF net, to decide if it is sound. Proof. Let PN be a free choice WF net. The extended net PN is also free choice. Therefore, the problem of deciding whether ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, 1995.

....P T nets. First, we introduce some basic definitions and useful properties. Second, we introduce some analysis techniques on P T nets. Readers familiar with Petri nets can browse through this section to become familiar with the notations used. An extensive treatment of Petri nets can be found in [19, 38, 39, 40]. 2.2 Basic definitions 2.2.1 P T nets A P T net is a directed graph with two kinds of nodes: transitions and places. Arcs in the graph always connect a node of one kind to a node of the other kind. Definition I (P T net) The triple N # (P, T, F) is a P T net iff: i. P is a finite, ....

....INCOME, LEU, and MOBILE) allow arbitrary non free choice constructs. Second, for a free choice WF net, it can be decided in polynomial time whether or not the net is sound, because it is possible to verify in polynomial time whether the corresponding short circuited WF system is live and bounded [19]. Given these two facts, one could envision a verification tool that focuses on free choice WF nets. However, for Woflan, we decided differently. One of the main requirements for Woflan mentioned in the introduction is that it is workflow product independent. Allowing nonfree choice WF nets ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....the P2P approach, and summarizing our plans for future work. 9 2 Preliminaries 2.1 Place Transition nets In this section, we define a variant of the classic Petri net model, namely labeled Place Transition nets. For a more elaborate introduction to Petri nets, the reader is referred to [21, 37, 39]. Let # be some universe of identifiers; let # be some set of action labels. # # # # # is the set of all visible labels. The role of # , the silent action, will be explained later. Definition 1 (Labeled P T net) A labeled Place Transition net is a tuple ### ###### ## where: 1. # # # is a ....

....the transitions of # # in two subsets ## and # # such that ## # # # # # # .# # # . ####### # # ## # # ## , # # # # # , and # # . ## # # # # # . # # because all stop transitions have been removed. Now we apply the well known exchange lemma (see for example page 23 in [21]) which allows us to project # # onto the transitions in ## and # # : # ## and # ## . Since # # . ## # # # # # . # #, the exchange lemma shows that we can first execute # ## followed by # ## . Let state # ## be the state after executing # ## , i.e. ## # ## # ### ## # ## # ## ## #. It ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....starting point a bc e Figure 8: A bill of materials. Figure 9: The construction of a workflow process definition based on Figure 8. for various kinds of analysis. For an overview of the many analysis methods developed for Petri nets the reader is referred to Murata [16] and Desel and Esparza [10]. These methods can be used to prove properties (e.g. safety properties, invariance properties, deadlocks) and to calculate performance measures (response times, waiting times, occupation rates, etc. In this way it is possible to evaluate alternative workflows. The rich theory of Petri nets ....

....using the algorithm. PN is safe (1 bounded) i.e. for each case the maximal number of tokens in a place is equal to one. This means that the places correspond to conditions which are either true (place contains one token) or false (place is empty) PN is (extended) free choice ([10]) i.e. if two transitions share an input place, then the sets of input places are identical. Free choice nets have some very elegant properties and correspond to workflows where parallelism and choice are separated. If in r is fused with out r , then the resulting net is strongly connected. ....

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, 1995.

....Its only goal is to provide a basis for the remainder of this paper. As mentioned in the introduction, for readers already familiar with Petri net theory, it is sufficient to browse through this section to get acquainted with notation. Good starting points for further reading on Petri nets are [19, 27, 41, 55, 59, 64, 65, 66]. 5.1 Notations for bags In this paper, bags are defined as finite multi sets of elements from some alphabet A. A bag over alphabet A can be considered as a function from A to the natural numbers IN such that only a finite number of elements from A is assigned a non zero function value. For some ....

....all their input places. The class of free choice P T nets combines a reasonable expressive power with strong analysis techniques. Consequently, free choice P T nets have been studied extensively in the literature. The most important results on free choice P T nets have been brought together in [27]. Except for Property 5.54, all results in this subsection appear in [27] The main theorems are given without proof. Some other results are accompanied with proofs, because the proofs illustrate the use of the main theorems. The results in this subsection show that traps, siphons, and ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....we point out some related work and discuss future extensions. 6 2 Preliminaries 2.1 Place Transition nets In this section, we define a variant of the classic Petri net model, namely labeled Place Transition nets. For a more elaborate introduction to Petri nets, the reader is referred to [13,30,31]. Let # be some universe of identifiers; let # be some set of action labels. # # # # # is the set of all visible labels. The role of # , the silent action, will be explained later. Definition 1 (Labeled P T net) A labeled Place Transition net is a tuple ### #### ## ## where: # # # is a ....

....the transitions of # # in two subsets ## and # # such that # # # # # # # # .# # # . ######### ## # # ## , # # # # # , and # # . ## # # # # # . # # because all stop transitions have been removed. Now we apply the well known exchange lemma (see for example page 23 in [13]) which allows us to project # # onto the transitions in ## and # # : # ## and # ## . Since # # . ## # # # # # . # #, the exchange lemma shows that we can first execute # ## followed by # ## . Let state # ## be the state after executing # ## , i.e. ## # ## # ### ## # ## # ## ## #. ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....Its only goal is to provide a basis for the remainder of this paper. As mentioned in the introduction, for readers already familiar with Petri net theory, it is sufficient to browse through this section to get acquainted with notation. Good starting points for further reading on Petri nets are [19, 27, 41, 55, 59, 64, 65, 66]. 5.1 Notations for bags In this paper, bags are defined as finite multi sets of elements from some alphabet A. A bag over alphabet A can be considered as a function from A to the natural numbers IN such that only a finite number of elements from A is assigned a non zero function value. For some ....

....all their input places. The class of free choice P T nets combines a reasonable expressive power with strong analysis techniques. Consequently, free choice P T nets have been studied extensively in the literature. The most important results on free choice P T nets have been brought together in [27]. Except for Property 5.54, all results in this subsection appear in [27] The main theorems are given without proof. Some other results are accompanied with proofs, because the proofs illustrate the use of the main theorems. The results in this subsection show that traps, siphons, and ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....IO soundness is decidable but also EXPSPACEhard ( 1] However, there are some interesting subclasses which allow for more efficient analysis techniques. For example, many workflow management systems only allow for workflow process definitions which correspond to free choice Petri nets ([11]) For this subclass and several others (cf. 1] the soundness property can be verified in polynomial time. t1 t2 t3 t4 t5 t6 t7 t8 p1 p2 p4 p5 p6 p3 i1 i2 t11 t12 t13 t14 t15 p11 p13 p12 ac1 ac3 o1 o2 sc1 t16 ac2 LWF1 LWF2 Figure 5: An IO sound interorganizational ....

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, 1995.

....over A. Moreover, X # Y and Y # X are defined in a straightforward manner. 2.2 Labeled Place Transition nets In this section, we define a variant of the classic Petri net model, namely labeled Place Transition nets. For a more elaborate introduction to Petri nets, the reader is referred to [24, 46, 53]. Let U be some universe of identifiers; let L be some set of action labels. Definition 2.1. Labeled P T net) An L labeled Place Transition net, or simply labeled P T net, is a tuple (P, T, F, #) where: 1. P # U is a finite set of places, 2. T # U is a finite set of transitions such that ....

....to free choice nets. The class of free choice P T nets combines a reasonable expressive power with strong analysis techniques. Consequently, free choice P T nets have been extensively studied in the literature. The most important results on free choice P T nets have been brought together in [24]. An example of a property which refers to the dynamics of a marked P T net is boundedness. Definition 2.10. Boundedness) A marked, labeled P T net (N, s) # N is bounded if and only if the set of reachable markings [N, s# is finite. In a bounded net, the number of tokens in any place is ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....using state of the art Petri net technology. 4.1 Introduction to Petri nets This section introduces the basic Petri net terminology and notations used in the remainder. Readers familiar with Petri nets can skip this section. Readers interested in more background material are referred to [DE95, Jen96, Mur89, Rei85]. The classical Petri net is a directed bipartite graph with two node types called places (graphically represented by circles) and transitions (graphically represented by thick lines) The nodes are connected via directed arcs. In this paper we consider Petri nets with arc weights. Arc weights ....

....clear which Petri net is considered. Note that the empty firing sequence is also allowed, i.e. M 1 [iM 1 . We use (PN ; M) to denote a Petri net PN with an initial state M . A state M 0 is a reachable state of (PN ; M) iff M [iM 0 . Let us define some standard properties for Petri nets (cf. [DE95, Jen96, Mur89, Rei85]) These definitions have been added to make the paper self contained. Liveness and boundedness correspond to the dynamic behavior of a Petri net in a given state. Definition 4.2 (Live) A Petri net (PN ; M) is live iff, for every reachable state M 0 and every transition t there is a state M ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, 1995.

....P T nets. First, we introduce some basic definitions and useful properties. Second, we introduce some analysis techniques on P T nets. Readers familiar with Petri nets can browse through this section to become familiar with the notations used. An extensive treatment of Petri nets can be found in [15,30]. 2.2. BASIC DEFINITIONS 2.2.1. NET STRUCTURE A P T net is a directed graph with two kinds of nodes: transitions and places. Arcs in the graph always connect a node of one kind to a node of the other kind. To identify the elements in a P T net, we introduce the set of identifiers U. Definition ....

....decide soundness. Theorem II. Free choice vs. soundness] Given a free choice WF net, it can be decided in polynomial time whether or not the net is sound. Proof Let N be a WF net. It is possible to verify in polynomial time whether the short circuited WF system (N, i] is live and bounded [15]. # Theorem III. Soundness and free choice vs. S coverability] Let N be a sound, free choice WF net. The shortcircuited WF net N is S coverable. Proof This follows directly from Theorem I and the fact that a net which is free choice, live, and bounded must be S coverable ( 15] # In ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, UK, 1995.

....that of the original life cycle. The third requirement is needed for the correctness of the transformation rule. In most practical examples, such as the examples in the next section, it is satis ed. An introduction to the free choice property and the class of free choice Petri nets can be found in [5]. The fourth and nal transformation rule, PJ1, shows that it is possible to insert behavior in between two parts of the original life cycle. If Nr is a net such that i) Nq and Nr share exactly one place p and one transition t with (t; p) in the ow relation of Nq , ii) all transitions of Nr ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....of a PN with a simpler one, while preserving certain semantic, behavioral or structural properties 1 See Section 5.1 for an example of how label splitting can be used also to increase the readability of the synthesized PN, by forcing it to belong to the sub class known as free choice. 4 [7, 54, 11, 41, 20]. In fact, as discussed in Section 4.5, we apply those structural reduction techniques in order to reduce the complexity of the TS representation when we derive the TS from a PN with the objective of optimizing it. It is known [3] that for ETS the complexity of synthesis of PNs is polynomial in ....

....can be performed. 4.5. 1 Encoding The dense encoding used for the markings of the PN of Figure 13 is based on the observation that the sets of places P 1 = fp 0 ; p 1 ; p 2 ; p 3 g, P 2 = fp 4 ; p 5 ; p 6 g and P 3 = fp 6 ; p 7 ; p 8 g define three state machines, SM1;SM2, and SM3, of the PN [27, 20] with the following sets of transitions T 1 = ft 1 ; t 2 ; t 3 ; t 4 g, T 2 = ft 1 ; t 5 ; t 6 g, and T 3 = ft 5 ; t 6 ; t 7 g, respectively. This information can be 27 structurally obtained by using algebraic methods [20] State machines correspond to place invariants of the PN and preserve ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

....A. Moreover, X # Y and Y # X are defined in a straightforward manner. 6 2.2 Labeled Place Transition nets In this section, we define a variant of the classic Petri net model, namely labeled Place Transition nets. For a more elaborate introduction to Petri nets, the reader is referred to [21, 41, 48]. Let U be some universe of identifiers; let L be some set of action labels. Definition 2.1. Labeled P T net) An L labeled Place Transition net, or simply labeled P T net, is a tuple (P, T, F, #) where: 1. P # U is a finite set of places, 2. T # U is a finite set of transitions such that ....

....to free choice nets. The class of free choice P T nets combines a reasonable expressive power 9 with strong analysis techniques. Consequently, free choice P T nets have been extensively studied in the literature. The most important results on free choice P T nets have been brought together in [21]. An example of a property which refers to the dynamics of a marked P T net is boundedness. Definition 2.10. Boundedness) A marked, labeled P T net (N, s) # N is bounded if and only if the set of reachable markings [N, s# is finite. In a bounded net, the number of tokens in any place is ....

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J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....obtain a place with multiple output arcs is the mapping of XOR split connectors onto Petri net constructs (see Figure 4) However, the rules given in Table 1 guarantee that the output transitions have identical sets of input places. Therefore, the Petri net is freechoice. Free choice Petri nets [9] are a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem [9] allows for the efficient analysis of liveness and boundedness. In freechoice Petri nets it is not allowed to mix choice and synchronization (see ....

....Table 1 guarantee that the output transitions have identical sets of input places. Therefore, the Petri net is freechoice. Free choice Petri nets [9] are a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem [9] allows for the efficient analysis of liveness and boundedness. In freechoice Petri nets it is not allowed to mix choice and synchronization (see Definition 12) Lemma 1 shows that in an event driven process chain choice and synchronization are separated. On the one hand, Lemma 1 is a positive ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, 1995.

....the original life cycle. The third requirement is needed in the correctness proof of the transformation rule. In most practical examples, such as the examples in the next section, it is satisfied. An introduction to the free choice property and the class of free choice Petri nets can be found in [5]. The fourth and final transformation rule, PJ1, shows that it is possible to insert behavior in between two parts of the original life cycle. If N r is a net such that i ) N q and N r share exactly one place p and one transition t with (t, p) in the flow relation of N q , ii) all transitions ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

No context found.

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

No context found.

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

No context found.

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....rules out logical errors such as deadlocks and livelocks. The notion of soundness is applicable to any workflow language. An interesting observation is that soundness corresponds to liveness and boundedness of the short circuited net [1] The latter properties have been studied extensively [41, 23]. As a result, powerful analysis techniques and tools can be applied to verify the correctness of a workflow design. Practical experience shows that many errors can be detected by verifying the soundness property. Moreover, Petri net theory can also be applied to guide the designer towards the ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....to rule PJ3 and is illustrated in Figure 6. If we extend a life cycle (N q , i] with a Petri net N r such that (1) no places are shared among both nets, 2) all new transitions have a label not in #(N q ) 3) the transitions in N q consuming tokens from N r obey 12 the free choice property ([6]) and (4) the result is still a life cycle, then the extended life cycle is a subclass of the original life cycle with respect to projection inheritance. Hence, we can add parts to the life cycle which are executed in parallel with the original life cycle while preserving projection inheritance. ....

....stated in Definition 3.1, then (N, i] is a subclass of (N # , i] with respect to projection inheritance, i.e. N, i] # pj (N # , i] For people not familiar with free choice Petri nets, requirement iii) may be hard to swallow. Using the rich theory of free choice Petri nets ([6]) it is easy to prove that [ p # ] is a so called home marking of (N # r , p # ] see [1] This implies that eventually every token consumed from place p # by N r is returned. If we abstract from the methods added by N r , then the replacement of the arc between t # and p # by N r ....

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of CambridgeTracts in Theoretical Computer Science. Cambridge University Press, Cambridge, 1995.

No context found.

DE95. J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....the results for free choice nets have been generalized are: equal conflict nets [TS93] and well handled nets [ES90] Weaker results (typically only one direction of a theorem for free choice nets) have been generalized to larger net classes. A typical example is the work on asymmetric choice nets [Hac72, BS87, DE95]. For example one direction of Commoner s Theorem can be generalized to asymmetric choice nets. In this paper, we explore further generalizations of asymmetric choice nets. In an asymmetric choice net, it is not allowed that two transitions compete for a token in a shared input place while they ....

....nets and show the equivalence of some of these net classes. Finally,we prove some results for one of the net classes identified and discuss the relevance of these results. 2 Basic concepts In this section, weintroduce the notation used in this paper and some of the standard results for Petri nets [Pet81, Rei85, Mur89, DE95]. A Petri net consists of a finite set of places P , a finite set of transitions T,andaflow relation F which relates transitions and places. A marking of a net associates a natural number with each place. This number represents the number of tokens residing at that place. In a textual ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free choice Petri nets,volume 40 of Cambridge tracts in theoretical computer science.Cambridge University Press, Cambridge, 1995.

...., # # # # , # # # # , ## # is strongly connected, ## # is a state machine, and for every # # # # and # # # : ### ## # # # ### ## # # # and ### ## # # # ### ## # # # . Definition 10 (S coverable) A Petri net is S coverable iff for any node there exist an S component which contains this node. See [10, 20] for a more elaborate introduction to these standard notions. 4 WF Nets In Figure 1 we indicated that a workflow has (at least) three dimensions. The controlflow dimension is the most prominent one, because the core of any workflow system is formed by the processes it supports. In the ....

....two or more alternatives. Therefore, we consider the non free choice construct shown in Figure 4 to be improper. In literature, the term confusion is often used to refer to the situation shown in Figure 4. Free choice Petri nets have been studied extensively (cf. Best [7] Desel and Esparza [10, 9, 12], Hack [15] because they seem to be a good compromise between expressive power and analyzability. It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem (Desel and Esparza [10] enables us to formulate the ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....A procedure which satisfies these requirements is called a sound workflow procedure. In [Aal97] this soundness property is defined formally and a technique is presented to verify this property in polynomial time. This technique is based on the rich theory developed for free choice Petri nets [Bes87, DE95]. If we analyze the procedure shown in Figure 1.9 using this technique, we detect an error. The workflow procedure is not sound: executing task A for a specific case followed by B1 and C1 results in a deadlock. For the workflow procedure shown in Figure 1.9 this result is trivial. However, for the ....

J. Desel and J. Esparza. Free choice Petri nets,volume 40 of Cambridge tracts in theoretical computer science.Cambridge University Press, Cambridge, 1995.

....24 to be improper. In literature, the term confusion is often used to refer to the situation shown in Figure 24. t2 t3 i t4 t5 t1 o c1 c2 c3 c4 Figure 24: A non free choice WF net containing a mixture of parallelism and choice. Free choice Petri nets have been studied extensively (cf. [Bes87, DE95, Des92, Esp90, Hac72]) because they seem to be a good compromise between expressive power and analyzability. It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem ( DE95] allows us to formulate the following corollary. ....

....studied extensively (cf. Bes87, DE95, Des92, Esp90, Hac72] because they seem to be a good compromise between expressive power and analyzability. It is a class of Petri nets for which strong theoretical results and efficient analysis techniques exist. For example, the well known Rank Theorem ([DE95]) allows us to formulate the following corollary. Corollary 1 A free choice WF net can be checked for soundness in polynomial time. Proof. See [Aal96a] Corollary 1 shows that, for free choice nets, there are efficient algorithms to decide soundness. It can also be shown that sound free choice ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free choice Petri nets, volume 40 of Cambridge tracts in theoretical computer science. Cambridge University Press, Cambridge, 1995.

....Different strategies have been used to calculate the state space: a) b) csc0 C DSr LDTACK LDS D DTACK LDTACK LDS DSr Q S R csc0 DTACK D Fig. 5. Implementations with 2 input gates Restrict the specification to a certain class of Petri nets, e.g. Free choice Petri nets [11], and use structural methods that can manipulate the state space by only analyzing the underlying graph of the net and without explicitly generating the states [33] Techniques for the efficient calculation of concurrency relations are crucial in this context [21] Annotate timing on the ....

....order reductions ( 15] stubborn sets [39] identification method [18] can abstract and ignore many of the irrelevant states for the verification of certain properties. Structural properties of Petri nets (e.g. place invariants) can provide fast upper approximation of the reachability space [6, 11, 29] and can be also used for dense variable encoding of states in the reachability graph. Structural reductions are useful as a preprocessing step in order to simplify the structure of the net before traversal or analysis, keeping all important properties. Unfoldings [19, 24] are finite acyclic ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

....to rule PJ3 and is illustrated in Figure 6. Extending a life cycle (N q , i] with a Petri net N r such that (1) no places are shared among both nets, 2) all new transitions have a label not in #(N q ) 3) the transitions in N q consuming tokens from N r obey the free choice property ([7]) and (4) the result is still a life cycle, yields a subclass under projection inheritance. Hence, we can add parts to the life cycle which are executed in parallel with the original life cycle while preserving projection inheritance. The third requirement is useful in the proof of the following ....

.... I (N, u) N # , v) # I (N, i] ## # I (N, u) # (N # , i] ## (N # , v) # u ( P q p # ) v ( P q p # ) # v p # is a home marking of (N r , u P r ) Using the theory of free choice nets (Home marking theorem, liveness and boundedness results, see [7]) in combination with the life cycle properties of Definition 3.1, it is possible to show that R satisfies the three requirements stated in Definition 2.6. 2 Example 5.5. Figure 8 illustrates the three transformation rules presented thus far. The first transformation rule can be used to prove ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

....if a free choice Petri net is live and bounded can be solved in O(n Delta m) time, where n and m are the number of places and transitions of the net, respectively. In turn, many analysis problems of live and bounded free choice Petri nets have also been shown to have polynomial time complexity [4]. Due to this series of results, the reachability problem of live and bounded free choice Petri nets, i.e. the problem of deciding if a given marking is reachable from the initial marking, has also been believed to be polynomial since around 1991. However, despite some very promising partial ....

....However, despite some very promising partial results, a proof has remained elusive. In [2] it was shown that when the Petri net is also cyclic 2 then the reachability problem can be reduced to solving a system of n ordinary linear equations with m variables, and is therefore polynomial. Later, [4] proved that every reachable marking can be reached from the initial marking by an occurrence sequence of length O(b Delta m 3 ) where b is the bound of the net, i.e. the maximum number of tokens that a reachable marking can put in a place. More recently, 11] provided a structural ....

[Article contains additional citation context not shown here]

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

No context found.

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

No context found.

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

No context found.

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

No context found.

J. Desel and J. Esparza. Free-choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.

No context found.

J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1995.

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