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

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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

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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