## Efficient Computation of Causal Behavioural Profiles using Structural Decomposition (2010)

Citations: | 8 - 5 self |

### BibTeX

@TECHREPORT{Weidlich10efficientcomputation,

author = {Matthias Weidlich and Artem Polyvyanyy and Jan Mendling and Mathias Weske},

title = { Efficient Computation of Causal Behavioural Profiles using Structural Decomposition},

institution = {},

year = {2010}

}

### OpenURL

### Abstract

Identification of behavioural contradictions is an important aspect of software engineering, in particular for checking the consistency between a business process model used as system specification and a corresponding workflow model used as implementation. In this paper, we propose causal behavioural profiles as the basis for a consistency notion, which capture essential behavioural information, such as order, exclusiveness, and causality between pairs of activities. Existing notions of behavioural equivalence, such as bisimulation and trace equivalence, might also be applied as consistency notions. Still, they are exponential in computation. Our novel concept of causal behavioural profiles provides a weaker behavioural consistency notion that can be computed efficiently using structural decomposition techniques for sound free-choice workflow systems if unstructured net fragments are acyclic or can be traced back to S- or T-nets.

### Citations

1433 |
Petri Nets: Properties, Analysis and Applications
- Murata
- 1989
(Show Context)
Citation Context ...e assume that each transition has one incoming and one outgoing flow arc. If this is not the case, we apply the pre-processing illustrated in Fig. 5, which preserves the behaviour of the system (cf., =-=[29]-=-) and, therefore, does not change the causal behavioural profile. Given a pre-processed WF-system (N, Mi) with N = (P, T, F ) and its WF-tree TN = (Ω, χ, t, b), each transition t ∈ T is a boundary nod... |

1001 | A survey of approaches to automatic schema matching
- Rahm, Bernstein
(Show Context)
Citation Context ...ontract & Close Record (b) Load Request for Quote Fig. 1. Example of two Petri net process models, (a) focussing on the business perspective, (b) depicting the workflow implementation schema matching =-=[4]-=- can be exploited as activities might be regarded as elements of a process model schema. In order to reason about the relation between two process models, existing notions of behavioural equivalence m... |

235 | Workflow Mining: Discovering Process Models from Event Logs
- Aalst, Weijters, et al.
(Show Context)
Citation Context ...ge body of research on behavioural relations for formal models specifying dynamic systems in general, and for Petri nets in particular. Focussing on the order of occurrence, the relations proposed in =-=[15]-=- for workflow mining are close to our relations, yet different. We base our definitions on the notion of an indirect weak order dependency, whereas the relations in [15] are grounded on a direct seque... |

143 | Property specification patterns for finite-state verification - Dwyer, Avrunin, et al. - 1998 |

118 | What Is a Petri Net
- Desel, Juhas
(Show Context)
Citation Context ...r process modelling and analysis. Note that Petri net based formalisations have been presented for (parts of) common process modelling languages, such as BPEL, EPCs, and UML, e.g., [8,9,10]. Based on =-=[7,11]-=-, we recall basic definitions.Efficient Computation of Causal Behavioural Profiles 3 Definition 1 (WF-net Syntax). ◦ A net is a tuple N = (P, T, F ) with P and T as finite disjoint sets of places and... |

97 |
The application of Petri nets to workflow management,” The
- Aalst
- 1998
(Show Context)
Citation Context ...ioural profiles along with experimental results is presented in Section 5. Finally, Section 6 reviews related work, before Section 7 concludes the paper. 2 Preliminaries We use workflow (WF-) systems =-=[7]-=- as our formal grounding, a class of Petri nets used for process modelling and analysis. Note that Petri net based formalisations have been presented for (parts of) common process modelling languages,... |

65 | Matching and Merging of Statecharts Specifications
- Nejati, Sabetzadeh, et al.
- 2007
(Show Context)
Citation Context ...ching. Recently, techniques including structural analysis and natural language processing to automatically identify such correspondences have been introduced for the domain of business process models =-=[2,3]-=-. Moreover, techniques known from the area of2 Matthias Weidlich, Artem Polyvyanyy, Jan Mendling, and Mathias Weske Request Offer from Subcontractor (B) Update Request for Offer (C) Create Project (G... |

62 | A technique of a state space search based on unfolding
- McMillan
- 1995
(Show Context)
Citation Context ... order in the behavioural profile. In order to cope with concurrency and the interleaving problem, the unfolding of a Petri net (or its prefix, respectively) might be exploited for behaviour analysis =-=[17,18]-=-. That is, a true concurrent model is created in which a transition (i.e., an event) corresponds to a certain occurrence of a transition in the original net. Events can be related as being in a weak c... |

61 | On the Semantics of EPCs: A Framework for Resolving the Vicious Circle
- Kindler
(Show Context)
Citation Context ... Petri nets used for process modelling and analysis. Note that Petri net based formalisations have been presented for (parts of) common process modelling languages, such as BPEL, EPCs, and UML, e.g., =-=[8,9,10]-=-. Based on [7,11], we recall basic definitions.Efficient Computation of Causal Behavioural Profiles 3 Definition 1 (WF-net Syntax). ◦ A net is a tuple N = (P, T, F ) with P and T as finite disjoint s... |

49 | The Refined Process Structure Tree
- Vanhatalo, Völzer, et al.
(Show Context)
Citation Context ... K B1 P2 B2 B3 P8 P3 R1 P12 F P10 P9 H R1 J P12 P4 P5 P9 P6 P7 P10 P11 (a) (b) Fig. 4. (a) A WF-system and its canonical fragments, (b) the RPST of (a) 4.1 The Refined Process Structure Tree The RPST =-=[20,21]-=- is a technique for detecting the structure of a workflow graph. A workflow graph can be parsed into a hierarchy of fragments with a single entry and a single exit, such that the RPST is a containment... |

48 | A feature-complete Petri net semantics for WSBPEL 2.0
- Lohmann
- 2008
(Show Context)
Citation Context ... Petri nets used for process modelling and analysis. Note that Petri net based formalisations have been presented for (parts of) common process modelling languages, such as BPEL, EPCs, and UML, e.g., =-=[8,9,10]-=-. Based on [7,11], we recall basic definitions.Efficient Computation of Causal Behavioural Profiles 3 Definition 1 (WF-net Syntax). ◦ A net is a tuple N = (P, T, F ) with P and T as finite disjoint s... |

46 |
Asurvey of behaviour and equivalence preserving re nements of Petri Nets
- Brauer, Gold, et al.
- 1990
(Show Context)
Citation Context ...process model towards a workflow model. These phenomena, in turn, can be quantified using the causal behavioural profile. Moreover, work on equivalence-preserving refinements for Petri nets, refer to =-=[38]-=- for a thorough survey, illustrates that common notions of equivalence are preserved solely under certain refinement operators. Similarly, work on net morphisms [39] and behaviour inheritance [40,41] ... |

38 |
S.: How do practitioners use conceptual modeling in practice? Data & Knowledge Engineering 58
- Davies, Green, et al.
- 2006
(Show Context)
Citation Context ...d net fragments are acyclic or can be traced back to S- or T-nets. 1 Introduction Process modelling has recently become one of the most extensively used approaches for capturing business requirements =-=[1]-=-. These requirements are typically refined and modified in an engineering process, resulting in a workflow model and software artefacts. A workflow model often defines activities of the business proce... |

35 |
A linear time implementation of SPQRtrees
- Gutwenger, Mutzel
- 2001
(Show Context)
Citation Context ...rkflow graph, its RPST can be computed in time linear to the number of edges of the graph [20,21]. The number of canonical fragments in the RPST is linear to the number of edges in the workflow graph =-=[21,27,28]-=-. Given the RPST of a WF-system, we iterate over all bond fragments and assign the behavioural annotations. Here, it suffices to check the type of the entry node, either a place or transition, and to ... |

35 |
A Survey of Equivalence Notions for Net Based Systems
- Pomello, Rozenberg, et al.
- 1992
(Show Context)
Citation Context ...avioural equivalence deserves further explanation. When applied in the context of model refinement and adaptation, the multitude of equivalence criteria from the linear time – branching time spectrum =-=[35,5]-=- has three major drawbacks. First and foremost, these notions yield a true or false answer, which has been criticised in [36]. Such notions cannot be applied to assess the amount of potential behaviou... |

30 |
Behavior-Consistent Specialization of Object Life Cycles
- Schrefl, Stumptner
- 2002
(Show Context)
Citation Context ... to [38] for a thorough survey, illustrates that common notions of equivalence are preserved solely under certain refinement operators. Similarly, work on net morphisms [39] and behaviour inheritance =-=[40,41]-=- shows that any extension of a net has to be done in a structured manner in order to preserve common equivalences. Third, notions of behavioural equivalence are computationally hard, which precludes a... |

29 | Tool support for verifying UML activity diagrams
- Eshuis, Wieringa
- 2004
(Show Context)
Citation Context ... Petri nets used for process modelling and analysis. Note that Petri net based formalisations have been presented for (parts of) common process modelling languages, such as BPEL, EPCs, and UML, e.g., =-=[8,9,10]-=-. Based on [7,11], we recall basic definitions.Efficient Computation of Causal Behavioural Profiles 3 Definition 1 (WF-net Syntax). ◦ A net is a tuple N = (P, T, F ) with P and T as finite disjoint s... |

29 | Measuring Similarity between Business Process Models
- Dongen, Dijkman, et al.
(Show Context)
Citation Context ...wo related Petri nets are preserved can be used as a behavioural similarity measure. Therefore, work on causal footprints as a behavioural abstraction for determining the similarity between processes =-=[43]-=- or on a trace-based similarity metric for process mining [36] is related. Further references on behavioural similarity can be found in [44]. Related work includes further applications of the tree-bas... |

25 | Dominators in linear time
- Alstrup, Harel, et al.
- 1999
(Show Context)
Citation Context ...e-choice). The co-occurrence relation for the causal profile is set directly in case of a T-system (cf., Lemma 4). In case of an S-system, dominators and post-dominators are determined in linear time =-=[30]-=-. Based thereon, co-occurrence is decided based on Lemma 5. For the case of acyclic free-choice WF-systems, co-occurrence is traced back to exclusiveness according to Lemma 6. That requires an iterati... |

21 |
K.: Unfoldings - A Partial-Order Approach to Model Checking
- Esparza, Heljanko
- 2008
(Show Context)
Citation Context ... order in the behavioural profile. In order to cope with concurrency and the interleaving problem, the unfolding of a Petri net (or its prefix, respectively) might be exploited for behaviour analysis =-=[17,18]-=-. That is, a true concurrent model is created in which a transition (i.e., an event) corresponds to a certain occurrence of a transition in the original net. Events can be related as being in a weak c... |

21 |
On-line maintenance of triconnected components with SPQR-trees
- Battista, Tamassia
- 1996
(Show Context)
Citation Context ...rkflow graph, its RPST can be computed in time linear to the number of edges of the graph [20,21]. The number of canonical fragments in the RPST is linear to the number of edges in the workflow graph =-=[21,27,28]-=-. Given the RPST of a WF-system, we iterate over all bond fragments and assign the behavioural annotations. Here, it suffices to check the type of the entry node, either a place or transition, and to ... |

19 | Merging business process models
- Rosa, Dumas, et al.
- 2010
(Show Context)
Citation Context ...ching. Recently, techniques including structural analysis and natural language processing to automatically identify such correspondences have been introduced for the domain of business process models =-=[2,3]-=-. Moreover, techniques known from the area of2 Matthias Weidlich, Artem Polyvyanyy, Jan Mendling, and Mathias Weske Request Offer from Subcontractor (B) Update Request for Offer (C) Create Project (G... |

18 |
Verification of workflow nets
- Aalst
- 1997
(Show Context)
Citation Context ...rcuit nets as WF-nets. Finally, we recall the soundness property, which requires WF-systems (1) to always terminate, and (2) to have no dead transitions (proper termination is implied for WF-systems) =-=[12]-=-. Definition 3 (Liveness, Boundedness, Soundness). ◦ A system (N, Mi) is live, iff for every reachable marking M ∈ [N, Mi〉 and t ∈ T , there exists a marking M ′ ∈ [N, M〉 such that (N, M ′ )[t〉. ◦ A s... |

17 |
handles, bridges and nets
- Esparza, Silva, et al.
- 1990
(Show Context)
Citation Context ...istinguish two cases: ◦ Let H be a path from p to t contained in ϑ. H is a PT-handle of Γ . In a live and bounded free-choice system, H is bridged to Γω through a TP-bridge K, cf., Proposition 4.2 in =-=[26]-=-. This implies that ϑ = γ; otherwise bond fragment ω contains path K that is not inside of a single child fragment, cf., [22,21]. Thus, ω has a single child fragment, a contradiction with the assumpti... |

15 | A Polynomial Algorithm to Compute the Concurrency Relation of Free-choiceSignal Transition Graphs
- Kovalyov, Esparza
- 1996
(Show Context)
Citation Context ... Computation of Causal Behavioural Profiles 7 in all markings, cf., Lemma 1 in [24]). Similarly, all transitions that are enabled concurrently in some reachable marking (cf., the concurrency relation =-=[16]-=-) are in interleaving order in the behavioural profile. In order to cope with concurrency and the interleaving problem, the unfolding of a Petri net (or its prefix, respectively) might be exploited fo... |

15 |
Simplified Computation and Generalization of the Refined Process Structure Tree
- Polyvyanyy, Vanhatalo, et al.
- 2011
(Show Context)
Citation Context ... K B1 P2 B2 B3 P8 P3 R1 P12 F P10 P9 H R1 J P12 P4 P5 P9 P6 P7 P10 P11 (a) (b) Fig. 4. (a) A WF-system and its canonical fragments, (b) the RPST of (a) 4.1 The Refined Process Structure Tree The RPST =-=[20,21]-=- is a technique for detecting the structure of a workflow graph. A workflow graph can be parsed into a hierarchy of fragments with a single entry and a single exit, such that the RPST is a containment... |

12 | Quantifying process equivalence based on observed behavior
- Medeiros, Aalst, et al.
- 2008
(Show Context)
Citation Context ...e of equivalence criteria from the linear time – branching time spectrum [35,5] has three major drawbacks. First and foremost, these notions yield a true or false answer, which has been criticised in =-=[36]-=-. Such notions cannot be applied to assess the amount of potential behavioural deviation. Second, it is well-known18 Matthias Weidlich, Artem Polyvyanyy, Jan Mendling, and Mathias Weske that interlea... |

12 | Inheritance of behavior
- Basten, Aalst
- 2001
(Show Context)
Citation Context ... to [38] for a thorough survey, illustrates that common notions of equivalence are preserved solely under certain refinement operators. Similarly, work on net morphisms [39] and behaviour inheritance =-=[40,41]-=- shows that any extension of a net has to be done in a structured manner in order to preserve common equivalences. Third, notions of behavioural equivalence are computationally hard, which precludes a... |

11 | Fundamentals of control flow in workflows
- Kiepuszewski, Hofstede, et al.
(Show Context)
Citation Context ...known that the free-choice and soundness properties are required to derive behavioural statements from the structure of a system, as both together imply a tight coupling of syntax and semantics (cf., =-=[23,24]-=-). Definition 9 (WF-Tree). Let (N, Mi) be a sound free-choice WF-system. The RPST with behavioural annotations, the WF-Tree of N, is a tuple TN = (Ω, χ, t, b), where: ◦ Ω is a set of all canonical fra... |

11 |
Workflow verification: Finding control-flow errors using petrinet-based techniques
- Aalst
- 2000
(Show Context)
Citation Context ...from Lemma 3 in [13] and the fact that sound free-choice WF-systems are safe (a place carries at most one tokenEfficient Computation of Causal Behavioural Profiles 7 in all markings, cf., Lemma 1 in =-=[24]-=-). Similarly, all transitions that are enabled concurrently in some reachable marking (cf., the concurrency relation [16]) are in interleaving order in the behavioural profile. In order to cope with c... |

9 |
H.M.W.E.: An alternative way to analyze workflow graphs
- Aalst, Hirnschall, et al.
- 2002
(Show Context)
Citation Context ...agment is either place or transition bordered, and that each loop fragment is place bordered. Note that a rigid fragment bordered with a place and a transition can still be free-choice and sound (see =-=[25]-=-). Lemma 1. Let TN = (Ω, χ, t, b) be the WF-tree of a sound free-choice WFsystem (N, Mi), N = (P, T, F ). No bond fragment ω ∈ Ω, t(ω) = B, has {p, t} boundary nodes, where p ∈ P and t ∈ T . Proof. As... |

9 | Similarity search of business process models
- Dumas, García-Bañuelos, et al.
- 2009
(Show Context)
Citation Context ...bstraction for determining the similarity between processes [43] or on a trace-based similarity metric for process mining [36] is related. Further references on behavioural similarity can be found in =-=[44]-=-. Related work includes further applications of the tree-based decomposition for behavioural models, e.g., model transformation [20] or model abstraction [22]. 7 Conclusions In this paper, we addresse... |

8 |
The triconnected abstraction of process models
- Polyvyanyy, Smirnov, et al.
- 2009
(Show Context)
Citation Context ...on behavioural similarity can be found in [44]. Related work includes further applications of the tree-based decomposition for behavioural models, e.g., model transformation [20] or model abstraction =-=[22]-=-. 7 Conclusions In this paper, we addressed the problem of finding a behavioural consistency notion that is weaker than existing notions of behavioural equivalence, but can be computed efficiently. Ou... |

8 | Process instantiation
- Decker, Mendling
- 2009
(Show Context)
Citation Context ...rom these models, we selected those that are non-trivial (more than one element), syntactically correct, free of deadlocks or livelocks (cf., [32]), and have unambiguous instantiation semantics (cf., =-=[33]-=-). We also normalised multiple start and end events, and replaced OR-split and OR-join connectors with AND connectors (which does not impact on the behavioural profile, but on the causal behavioural p... |

8 |
Refinement of actions and equivalence notions for concurrent systems
- Glabbeek, Goltz
- 1998
(Show Context)
Citation Context ... deviation. Second, it is well-known18 Matthias Weidlich, Artem Polyvyanyy, Jan Mendling, and Mathias Weske that interleaving equivalences are not invariant under forgetful refinements of activities =-=[37]-=-, i.e., projection of activities. However, our initial example shows that projections are a substantial part of refining and adapting a process model towards a workflow model. These phenomena, in turn... |

6 |
Mendling. Change Propagation in Process Models using Behavioural Profiles
- Weidlich, Weske
(Show Context)
Citation Context ...ave to be seen as core requirements on such notions. It is worth to mention that we already showed how behavioural profiles can be applied to support change propagation between related process models =-=[19]-=-. 4 Graph Decomposition Techniques for WF-Systems First, Section 4.1 introduces the Refined Process Structure Tree (RPST), a structural decomposition technique for workflow graphs. Second, Section 4.2... |

4 |
Verification of the SAP reference models using EPC reduction, statespace analysis, and invariants
- Dongen, Jansen-Vullers, et al.
- 2007
(Show Context)
Citation Context ...lity of the SAP R/3 system and comprises 737 EPC models. From these models, we selected those that are non-trivial (more than one element), syntactically correct, free of deadlocks or livelocks (cf., =-=[32]-=-), and have unambiguous instantiation semantics (cf., [33]). We also normalised multiple start and end events, and replaced OR-split and OR-join connectors with AND connectors (which does not impact o... |

2 |
The Linear Time – Brancing Time Spectrum I. The semantics of concrete, sequential processes
- Glabbeek
- 2001
(Show Context)
Citation Context ...ation and trace equivalence assume the set of all traces or the branching structure as essential behavioural characteristics that have to be preserved. However, these notions are computationally hard =-=[5]-=-, which is particularly a problem for process models including many activities. Furthermore, these notions only provide information whether behaviour is equivalent or not, but do not describe how stro... |

2 |
M.: Computation of behavioural profiles of process models
- Weidlich, Mendling, et al.
- 2009
(Show Context)
Citation Context ...ural Profile This section introduces causal behavioural profiles. They are based on the notion of behavioural profiles, which we recall in Section 3.1. We introduced these profiles in an earlier work =-=[13]-=- to reason on execution ordering constraints only. Thus, optionality of transition execution or causality between transitions is not captured. These aspects are addressed by the novel concept of a cau... |

1 |
The state explosion problem. In: Petri Nets. Volume 1491 of LNCS
- Valmari
- 1996
(Show Context)
Citation Context ...nt. Both could be mapped to an S-system and, therefore, be handled as introduced in Section 5.2. To illustrate the extent to which the models of our collection suffer from the state explosion problem =-=[34]-=-, Fig. 8 shows the average computation time for a naive creation of the reachability graph (RG). While all reachability graphs are finite (due to soundness of the WF-systems), computation takes up to ... |

1 |
A.: Analyzing Semantics of Concurrent Hardware Specifications
- Rosenblum, Yakovlev
- 1989
(Show Context)
Citation Context ...putational efficiency. Relations similar to those of the behavioural profile have been proposed to reason on the consistency of hardware specifications and requirements imposed by operational modules =-=[42]-=-. To this end, transitions of a Petri net can be classified as being sequential or parallel depending on whether there is an order between all their occurrences in all traces. In addition, these relat... |