# The Analysis Method about Change Domain of Business Process Model Based on the Behavior Profile of Petri Net

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2 944 Fang et al : Optimal Analysis Method about Change Domain... activity nodes; it didn t make much analysis of the dynamic changes in behavior cased by the activities. In this paper, our goal is to build a process model based on Petri nets, giving its definition and related concepts, combining with Petri net dynamic behavior characteristics and behavior profile that captures control relations between each pair of activities from corresponding models. First, we can find the suspicious area in source model, and then construct some algorithms to searching and narrowing the area. Finally, we determine the change range and get the change node. The reminder of this article is structured as follows. Section 2 introduces the basic notations. According the relate knowledge of Petri nets and behavior profile, giving two important algorithms to determine the change node in Section 3. We report our findings of applying these algorithms to the reference model in section 4. Finally, section 5 concludes the paper and provides an outline on the future work. 2. Basic conception This part introduces some basic concepts used in this article, and other related concepts can be found in [1,5,6]. First, we introduce the nation of a process Petri net used throughout the paper. Second, we define behavior profiles to capture the behavior characteristics of the process network. Finally, introduces the correspondence between the process models network. Definition 1(Process Petri Net) A process Petri net is a tuple BP p =(P, T, F, C) with P is a set of condition nodes, T is a set of change activity nodes, such that P, T and P T = ; F (P T ) (T P ) is the flow relation; C = {od,or,pl,cy} as the type of process network structure, ie order, or, parallel and cycle structures. A process Petri net can be made of those four structures from a business process. Given an initial marking of a Petri net, it exists a firing sequence because of an occurrence of rule. There are some related concepts about Petri net, like the set of all input and output places of a transition, respectively, markings, and firing sequences and reachable and so on can refer to [6]. The notion of observed execution sequences of process Petri net is formalized as follows: Definition 2(Execution Sequence) the execution sequence T pm for a process Petri net BP p =(P, T, F, C), is the set of all firing sequences σ = t 1 t 2...t n 1 t n > 0, n N for which holds M 0 [σ M n. The above definition explains if a process model Petri net BP p =(P, T, F, C) exists an observed execution sequence, there is a path from start activity node to the end one, to ensure that the process model network is live, not deadlock or dead transition. Behavior profile captures the behavior relation between processes in graze-fine. The net proposed in this paper contains four types of relations; they are all established on the basis of feasible trace. Two nodes or flow relation of a process model net are in the same feasible trace, if there exists a sequence in which one node occurs after the other. Definition 3(Feasible Trace) A process Petri net BP p = (P, T, F, C), execution sequence T pm, τ = n 1 n 2...n k is a set of nodes, if (x, y) ((N F )(N F )), such that j (1,...,k 1), j < h k, which holds n j = x, n h = y,soτ a feasible trace, and τ T pm, holds x y. The behavior profile is grounded on the notion of feasible trace between activity transition nodes in a process Petri net. This relation requires the existence of such a trace and does not have to hold for all traces of the model. Depending on how two activity transition nodes of a process Petri net are related by feasible trace, we define four relations forming the behavior profile. Definition 4[2], (Behavior Profile) Let BP p =(P, T, F, C) be a process Petri net, x, y are activity transition nodes, (x, y) ((N F )(N F )) is in one of the following relation: The strict order relation (x, y), ifx y, and y x; The exclusiveness relation +(x, y), ifx y, y x; The parallel relation (x, y), ifx y, x z; The interleaving order relation (x, y), ifx y, y x. The set of all four relations is the behavior profile of BP p. Note that we say that a pair (x, y) is in reverse order relation, denoted by 1 (x, y), ify x and x y. A process Petri net BP p =(P, T, F, C), M 0 is an initial marking, we can determine the relationship between activity transition nodes in process model. The exemplary process in Figure 1 illustrates the relations of the behavior profile for two dedicated activity transition nodes A and B. The Figure 1(a) shows that the strict order relation enforces both nodes occur together or neither of them occurs. In the Figure 1(b), and order relation captures the fact that all occurrences of both activity transition nodes are ordered in all firing sequences reachable from the initial marking, i.e. the occurrence of A lead to the occurrence of B, denoted as A B. In the Figure 1(c), both activity transitions are exclusive to each other, A+B. That is, both nodes are never observed together in any firing sequence, or there may be a firing sequence that contain none of them. In the Figure 1(d) shows the parallel order relation between the two activity condition nodes that can be observed in two branch line running in parallel rode in a firing sequence under the same initial marking denoted A B. The last one exemplify interleaving order of two activity transition nodes, A B. It does not necessarily imply the concurrent enabling of two nodes in a certain marking, but the two nodes can exist in any order in a firing sequence. It might also result from cyclic structure.

3 Appl. Math. Inf. Sci. 6-3S, No. 3, (2012) / (a) (b) Algorithm 1 Looking for the set of corresponding transitions Input: BP p1 =(P 1,T 1,F 1,C 1) process Petri net 1 BP p2 =(P 2,T 2,F 2,C 2) process Petri net 2. Output: A, the set of corresponding transitions. 1: According to the definition 5 obtain a suspicious area W 01, marked the nodes a 01a 02a 03 a 0n 1a 0n, the area of corresponding source model is W 01. 2: From a 01 to consider its behavior relationship with the next node. 3: Compare the behavior relationship in source model, if a 01 a 02, the suspicious area is W 01 {a 01}. 4: When meet branching structure, if +(a 0i 1,a 0i), 2 i n, choose one branching compare to the correspondent structure of source model, if not satisfy the order relation, a 0i 1 is a suspicious node, else suspicious area is W 01 {a 01,a 0n,a 0i}; if (a 0i 1,a 0i) or (a 0i 1,a 0i), 2 i n, return to step 2. 5: Get a change region W 01 {a 01,a 0n,a 0i,...}, 2 i n, a set of suspicious node Q. Output change region W 0 and suspicious nodes Q. (c) (d) Figure 1 The structure relation of behavior profile Initially, the change region is a subnet of the target model, and it is narrowed using the correspondence between target model and source model. In order to find the change region in the target model, first and foremost, we have to clarify the notion of the corresponding relation between process models and propose the correspondences between activity transition nodes in process Petri nets based on behavior profile. Definition 5(Correspondence Relation based on Transition Pairs). Two process Petri nets BP p1 =(P 1,T 1,F 1,C 1 ) and BP p2 = (P 2,T 2,F 2,C 2 ), Correspondence relation T 1 T 2, if there is a mapping when (t a,t s ), (t b,t y ) and t 1 T 1, t 2 T 2 which holds t 1 t 2, then (t a = t b ) (t x = t y ), include all activity transition nodes in process Petri net. In order to find the pairs of activity transition nodes that satisfy the correspondence relation between source model and target model, according the dynamic thinking of Petri net, given the algorithm to derive the nodes that have the correspondence relation. The algorithm is showed in algorithm 1. For a business process, a change operation in target model is reflected in its behavior profile, i.e., its characteristic relations. Therefore, these relations localize the change in the target model. Under the assumption that the target model and the source model have been aligned to some extent, we can localize the change region in target model by the corresponding activities. Definition 6[5], (Change Region) A process Petri net BP p = (P, T, F, C), a change region BP p =(P,T,F,C ) is a subnet of BP p which holds P P, T T,F F, C C and BP p BP p. 3. The analysis method of looking for change domain based on the dynamic behavior of Petri Net A change operation in the source business process model is reflected in its behavior profile, i.e., its characteristic relations. So these relations locate the change in the source process model. Because the source and the target process model have been aligned to some extent, in order to locate a change region in the target process model, using the characteristic relations for the corresponding activities in the target process model. This region identifies a part of the target model in which the change of the source process model has to be realized [6,7]. Weidlich et. al [5, 8] determined the change region might either be a set of flow arcs of the target model or an empty set. The former indicates that there are already flow arcs in the model that fulfil the requirements of the behavior profile with respect to the potential change. Therefore, all these flow arcs qualify for representing the change of the source model in the target model. Note that these flow arcs are not necessarily part of a connected subgraph of the process model. Instead, there might be multiple areas in the target model that qualify for the realization of the change. In case the set is empty, the target model does not yet contain a flow arc satisfying the behavioral requirements. However, it is always possible to insert flow arcs according behavioral requirements. In this case, the boundary nodes and inter-boundary nodes guide the adaptation of the target process model. The former impose requirements regarding

4 946 Fang et al : Optimal Analysis Method about Change Domain... the strict order relation, whereas the exclusiveness and observation concurrency relation have to be considered for the latter. Some proposed methods mainly adopted the static behavior methods, the suspicious area [9, 10] is analyzed by the appointed nodes, but this is a particular process.in order to localize the change region in a business process, we propose a dynamic behavior analysis method. First, according to definition 1,we transform the business into process Petri net. Second, determine the suspicious area based on the correspondence between source model and target model. Third, narrow the suspicious area gradually by the constraints of behavior profile. Finally, extract all the execution sequences that through the suspicious area, we use behavior relations [11] and the dynamic behavior characteristics of Petri net to find the smallest change region and change nodes [12 14]. We give Algorithm 2 to derive the optimal change region. Based on Algorithms 2, we propose Algorithm 3 to find the set of change nodes using the characteristics of the dynamic behavior of Petri net. Algorithm 2 Determining the change region in target model Input: BP p0 =(F 0,T 0,F 0,C 0), source model BP p =(P, T, F, C), target model Output: W 0, change region 1: Get a suspicious area W 01 from Algorithm 1, marked the nodes a 01a 02a 03 a 0n 1a 0n, the area of corresponding source model is W 01; 2: From a 01 to consider its behavior relationship with the next node; 3: Compare the behavior relationship in source model, if a 01 a 02. suspicious area is W 01 {a 01}; else 4: From a 0n to consider its behavior relationship with the last node st the same time; 5: Compare the behavior relationship in source model, if a 0n 1 a 0n 1, suspicious area is W 01 {a 01,a 0n}; else, continue 6: When meet branching structure, if +(a 0,i 1,a 0i), 2 i n, choose one branching compare to the correspondent structure of source model, if not satisfy the order relation, a 0i 1 is a suspicious node,else suspicious area is W 01 {a 01,a 0n,a0i}, turn to step 2; 7: If (a 0i 1,a 0i) or (a 0i 1,a 0i), 2 i n, turn to step 2; 8: Get a change region W 01 {a 01,a 0n,a 0i,...}, 2 i n, a set of suspicious node Q. Output change region W 0 and suspicious nodes Q. Algorithm 3 Looking for the set of change node Input: W 0, change region Q, a set of suspicious node S =(N,M 0), a initial marking Output: N 0, a set of change node 1: According to definition 1 transform the change region W 0 in target model into process petri net; 2: Given a initial marking S = (N,M 0) to target model BP p = (P, T, F, C), get all firing sequences σ 1σ 2 σ m that through the suspicious node and change region, W c = W 01 {a 01,a 0n,a 0i,...}, 2 i n; 3: Select a sequence σ i, 1 i m, not repeat choose two different condition place nodes p i, p j, i<j; 4: If p i or p i, S 1 = p i p i p j p i..., i.e. the set of all input transition of p i and p j, and the set of all input places of transitions and so on; else S 1 = σ i: 5: If p i or p i, S 2 = p i p i p j p j..., i.e. the set of output transition of p i and p j,and the set of all output transitions of places and so on; else S 1 = σ i. 6: Return to step 3. is the initial suspicious area from the correspondence between models, Further on, we consider the constraint relations of activity transitions between models based on behavior profile, using Algorithm 2 to narrow the dashed box part until we find the smallest change region in target model which shown in Figure 4. According to Algorithm 3, we collect all observed execution sequences that through W 0 in Figure 4. There are three execution sequences fragment, i.e. t 7 t 9 t 15, t 8 t 13 t 15 and t 8 t 11 t 12. Take t 8 t 13 t 15 for example, given two condition places p 11 and p 13, The first step, for the place p 11, Algorithm 3 returns the activity transitions T in p 11 and the input places of these transitions T until n i W min, so does p 13. Then, move backwards adding the places and transitions become a submodules S 1 which shown in left side of Figure 5. The second step, for the place p 11, Algorithm 3 moves forwards adding the transitions T in p 11 and the output places of these transitions T until n j W min, so does p 13. Then we get a sub-modules S 2 which shown in right side of Figure 5. The third step, the change node under the sequence t 8 t 13 t 15 is the intersection of S 1 and S 2, i.e. S 1 S 2 = {t 13 }. According the same analysis in the above method, we can also choose p 8 and p 13, the intersection is {t 9 }, Any other group of places are the empty set. Finally, the change region in the target model is {t 9 p 13 t 13 }, and the set of change nodes is {t 9,t 13 }. 5. Conclusion 4. Case study In this paper, we select source model and target model in [5] as our examples. First, the Petri net of source model and target model are shown in Figure 2 and Figure 3, According to Algorithm 1, the dashed box part in Figure 3 In order to adapt to rapidly changing business needs, looking for change nodes in business processes has a certain practical significance. In [5],they illustrate a change region can be localized by a dedicated node which is determined from the static respect. In this paper, we give a structure of business process model based on Petri net and propose

5 Appl. Math. Inf. Sci. 6-3S, No. 3, (2012) / Figure 2 Petri net of source business process model Figure 3 Petri net of target business process model Figure 4 The smallest change region

6 948 Fang et al : Optimal Analysis Method about Change Domain... (a) (b) Figure 5 Backward and forward set of p 11 and p 13 the behavior profile of process Petri net. First of all, we give Algorithm 1 to discuss the correspondence between activity place nodes of source model and target model. Then combine the behavior profile and the dynamic behavior characteristics of Petri net to looking for a change region in Algorithm 2. Finally, Algorithm 3 is proposed to narrow the change region gradually and find a set of change node which based on Algorithm 2. Our approach overcomes the shortcomings that a process model can only be determined in a static node. And give a formal analysis of the dynamic behavior of the process model. Instance analysis shows that our method has certain validity. As a future work, we plan to use our approach to check the consistency between the process models and carry on the amendment of the model with the change node. We can also optimize a target model gradually to make it close to its source model. And we hope that these operations can be realized automated processing in the near future. Acknowledgement We would like to thank the support of the National Natural Science Foundation of China under Grant No , No , No , No , No and No , the National High-Tech Research and Development Plan of China under Grant No.2009AA01Z4-01, the Natural Science Foundation of Educational Government of Anhui Province of China (KJ2011A086 and KJ2012A073), Anhui Provincial Natural Science Foundation( MF105), Anhui Provincial Soft Science Foundation( ), the Natural Science Foundation of Shanxi (Nos ). References [1] M. Weidlich, J. Mendling and M. Weske, IEEE Transactions Softare Engineering 37, 410 (2011). [2] M.Weidlich, A. Polyvyanyy, N. Desai, J. Mendling and M. Weske, Information Systems 36, 1009 (2011). [3] M. Weidlich and J. Mendling, Information Systems 37, 80(2012). [4] M. Weidlich, A. Polyvyanyy, N. Desai and J. Mendling, Lecture Notes in Computer Science 6051, 499 (2010). [5] M. Weidlich, M. Weske and J. Mendling, Proc of IEEE International Conference on Services Computing, 33(2009). [6] T. Murata, Proc. IEEE. 11, 541 (1989). [7] R. Dijkman, M. Dumas and C. Ouyang, Information and Software Technology 51, 1281 (2009). [8] R. M. Dijkman, Lecture Notes in Computer Science 5240, 261 (2008). [9] E Kindler, Lecture Notes in Computer Science 3080, 82 (2004). [10] B. Weber, S. Rinderle and M. Reichert, Lecture Notes in Computer Science 4495, 574 (2007). [11] M. Lorens, J. Oliver, J. Silva, S. Tamarit and G. Vidal, Electronic Notes in Theoretical Computer Science 233, 153 (2008). [12] M. Weidlich, F. Elliger and M.Weske, Lecture Notes in Computer Science 6551, 101 (2011). [13] X.W.Fang, C.J. Jiang, Z.X.Yin and X.Q.Fan, Computer Science and Information Systems 8, 843 (2011). [14] K. Johannes, K. Markus and S. Tarja, Software Practice & Experience 40, 701 (2010).

7 Appl. Math. Inf. Sci. 6-3S, No. 3, (2012) / Xianwen Fang received his M.A. degree from Shandong University of Science and Technology, China, in 2004, and PhD. degree in the key Lab of Service Computing at Tongji University in He is currently a Professor with the Department of Computer Science and Engineering, Anhui University of Science and Technology, China. His research interests include Petri net, trustworthy software and Web services. He has published more than 60 papers in domestic and international academic journals and conference proceedings. These papers are embodied more than 40 times by SCI and EI and are cited more than 80 times by others. Wenjun Hao received the M.A. degree from Anhui University of Science and Technology, China, in She is currently a lecturer with the Department of Computer Science and Engineering, Anhui University of Science and Technology, China. Her current areas of research are concurrent theory, Petri net and formal verification of software. Xiaoqin Fan received her M.A. degree from TaiYuan University of Science and Technology, China, in 2002, and PhD. degree in the key Lab of Service Computing at Tongji University in Her research interests include Petri net and Web services. Zhixiang Yin received her M.A. degree from Nanjing Normal University of SChina in 1996, and PhD. degree in the Huazhong University of Science and Technology in His research interests include Petri net and trusted software.

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