## 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.

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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 ... |

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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... |

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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... |

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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... |

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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... |

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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 ... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

6 | Mendling. Change Propagation in Process Models using Behavioural Profiles
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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... |

3 |
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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... |

2 |
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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... |

1 |
The state explosion problem. In: Petri Nets. Volume 1491 of LNCS
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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
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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... |