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New Region-Based Algorithms for Deriving Bounded Petri Nets
March 2010 (vol. 59 no. 3)
pp. 371-384
Josep Carmona, Universitat Politècnica Catalunya, Barcelona
Jordi Cortadella, Universitat Politècnica Catalunya, Barcelona
Mike Kishinevsky, Intel, Hillsboro
The theory of regions was introduced in the early nineties as a method to bridge state and event-based models. This paper tackles the problem of deriving a Petri net from a state-based model, using the theory of regions. Some of the restrictions required in the traditional approach are dropped in this paper, together with significant extensions that make the approach applicable in new scenarios. One of these scenarios is Process Mining, where accepting (discovering) additional behavior in the synthesized Petri net is sometimes valued. The algorithmic emphasis used in this paper contributes to the demystification of the theory of regions as been only a good theoretical exercise, opening the door for its application in the industrial domain.

[1] Genet,∼jcarmonagenet.html , 2009.
[2] A. Arnold, Finite Transition Systems. Prentice Hall, 1994.
[3] E. Badouel and P. Darondeau, “Theory of Regions,” Petri Nets, W.Reisig and G. Rozenberg, eds., pp. 529-586, Springer, 1998.
[4] R. Bergenthum, J. Desel, R. Lorenz, and S. Mauser, “Synthesis of Petri Nets from Finite Partial Languages,” Fundamenta Informaticae, vol. 88, no. 4, pp. 437-468, 2008.
[5] R. Bergenthum, J. Desel, R. Lorenz, and S. Mauser, “Process Mining Based on Regions of Languages,” Proc. Fifth Int'l Conf. Business Process Management, pp. 375-383, Sept. 2007.
[6] N. Busi and G.M. Pinna, “Characterizing Workflow Nets Using Regions,” Proc. Int'l Symp. Symbolic and Numeric Algorithms for Scientific Computing, pp. 399-406, 2006.
[7] B. Caillaud “Synet: A Synthesizer of Distributable Bounded Petri-Nets from Finite Automata,” synet/, 2002.
[8] J. Carmona, J. Cortadella, and M. Kishinevsky, “A Region-Based Algorithm for Discovering Petri Nets from Event Logs,” Proc. Int'l Conf. Business Process Management (BPM), M. Dumas, M. Reichert, and M.C. Shan, eds., pp. 358-373, 2008.
[9] J. Carmona, J. Cortadella, M. Kishinevsky, A. Kondratyev, L. Lavagno, and A. Yakovlev, “A Symbolic Algorithm for the Synthesis of Bounded Petri Nets,” Proc. 29th Int'l Conf. Applications and Theory of Petri Nets (PETRI NETS '08), pp. 92-111, 2008.
[10] T.H. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms. The MIT Press and McGraw-Hill Book Company, 1989.
[11] J. Cortadella, M. Kishinevsky, L. Lavagno, and A. Yakovlev, “Deriving Petri Nets from Finite Transition Systems,” IEEE Trans. Computers, vol. 47, no. 8, pp. 859-882, Aug. 1998.
[12] P. Darondeau, “Region Based Synthesis of P/T-Nets and its Potential Applications,” Proc. 21st Int'l Conf. Application and Theory of Petri Nets, pp. 16-23, 2000.
[13] P. Darondeau, “Unbounded Petri Net Synthesis,” Lectures on Concurrency and Petri Nets, J. Desel, W. Reisig, and G. Rozenberg, eds., pp. 413-438, Springer, 2003.
[14] P. Darondeau, “Distributed Implementations of Ramadge-Wonham Supervisory Control with Petri Nets,” Proc. 44th IEEE Conf. Decision and Control, 2005, and 2005 European Control Conference (CDC-ECC '05), pp. 2107-2112, Dec. 2005.
[15] P. Darondeau Private Communication, 2008.
[16] J. Desel and W. Reisig, “The Synthesis Problem of Petri Nets,” Acta Informatica, vol. 33, no. 4, pp. 297-315, 1996.
[17] D.L. Dill, “Trace Theory for Automatic Hierarchical Verification of Speed Independent Circuits,” ACM distinguished dissertations, MIT Press, 1989.
[18] A. Ehrenfeucht and G. Rozenberg, “Partial (Set) 2-Structures. Part I, II,” Acta Informatica, vol. 27, pp. 315-368, 1990.
[19] P.W. Hoogers, H.C.M. Kleijn, and P.S. Thiagarajan, “A Trace Semantics for Petri Nets,” Information and Computation, vol. 117, no. 1, pp. 98-114, 1995.
[20] R.M. Karp and R.E. Miller, “Parallel Program Schemata,” J.Computer and System Sciences, vol. 3, pp. 147-195, 1969.
[21] N.A. Lynch and M.R. Tuttle, “Hierarchical Correctness Proofs for Distributed Algorithms,” Proc. Sixth Ann. ACM Symp. Principles of Distributed Computing, pp. 137-151, Aug. 1987.
[22] R. Milner, Communication and Concurrency. Prentice-Hall, 1989.
[23] M. Mukund, “Petri Nets and Step Transition Systems,” Int'l J.Foundations of Computer Science, vol. 3, no. 4, pp. 443-478, 1992.
[24] S.M. Nowick and D.L. Dill, “Automatic Synthesis of Locally-Clocked Asynchronous State Machines,” Proc. Int'l Conf. Computer-Aided Design (ICCAD), pp. 318-321, Nov. 1991.
[25] C.A. Petri, “Kommunikation mit Automaten,” PhD thesis, Bonn, Institut für Instrumentelle Mathematik (technical report Schriften des IIM Nr. 3), 1962.
[26] A. Rozinat and W.M.P. van der Aalst, “Conformance Checking of Processes Based on Monitoring Real Behavior,” Information Systems, vol. 33, no. 1, pp. 64-95, 2008.
[27] M.H.T. Beek, C.A. Ellis, J. Kleijn, and G. Rozenberg, “Synchronizations in Team Automata for Groupware Systems,” Computer Supported Cooperative Work, vol. 12, no. 1, pp. 21-69, 2003.
[28] W. van der Aalst, V. Rubin, H. Verbeek, B. van Dongen, E. Kindler, and C. Günther, “Process Mining: A Two-Step Approach to Balance between Underfitting and Overfitting,” Technical Report BPM-08-01, BPM Center, 2008.
[29] W.M.P. van der Aalst and C.W. Günther, “Finding Structure in Unstructured Processes: The Case for Process Mining,” Proc. Seventh Int'l Conf. Application of Concurrency to System Design (ACSD), T. Basten, G. Juhás, and S.K. Shukla, eds., pp. 3-12, 2007.
[30] W.M.P. van der Aalst, T. Weijters, and L. Maruster, “Workflow Mining: Discovering Process Models from Event Logs,” IEEE Trans. Knowledge and Data Eng., vol. 16, no. 9, pp. 1128-1142, Sept. 2004.
[31] J.M.E.M. van der Werf, B.F. van Dongen, C.A.J. Hurkens, and A. Serebrenik, “Process Discovery Using Integer Linear Programming,” Proc. 29th Int'l Conf. Applications and Theory of Petri Nets (PETRI NETS '08), pp. 368-387, 2008.
[32] B.F. van Dongen, A.K.A. de Medeiros, H.M.W. Verbeek, A.J.M.M. Weijters, and W.M.P. van der Aalst, “The Prom framework: A New Era in Process Mining Tool Support,” Proc. Int'l Conf. Applications and Theory of Petri Nets (ICATPN), G. Ciardo and P.Darondeau, eds., pp. 444-454, 2005.
[33] Proc. 29th Int'l Conf. Applications and Theory of Petri Nets (PETRI NETS '08), K.M. van Hee and R. Valk, eds., 2008.
[34] A. Weijters, W. van der Aalst, and A.A. de Medeiros, “Process Mining with the Heuristics Miner-Algorithm,” Technical Report WP 166, BETA Working Paper Series, Eindhoven Univ. of Tech nology, 2006.

Index Terms:
Petri nets, transition systems, theory of regions, synthesis, process mining, bisimulation.
Josep Carmona, Jordi Cortadella, Mike Kishinevsky, "New Region-Based Algorithms for Deriving Bounded Petri Nets," IEEE Transactions on Computers, vol. 59, no. 3, pp. 371-384, March 2010, doi:10.1109/TC.2009.131
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