Abstract
We investigate structural equivalences on places of P/T nets that allow reductions compatible with bisimilarity. This comes with a study of two kinds of reductions: fusion of equivalent places, and replacement of some places by other ones. When effectivity issues are considered, we are lead to a variant of place bisimulation that takes into account a set of “relevant” markings.
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C. Autant, Z. Belmesk, and Ph. Schnoebelen. Strong bisimilarity on nets revisited. In Proc. Parallel Architectures and Languages Europe (PARLE’91), Eindhoven, NL, June 1991, vol. II: Parallel Languages, volume 506 of Lecture Notes in Computer Science, pages 295–312. Springer, 1991.
C. Autant, W. Pfister, and Ph. Schnoebelen. Place bisimulations for the reduction of labeled Petri nets with silent moves. In Proc. 6th Int. Conf. on Computing and Information (ICCI’94), Trent University, Canada, May 1994, pages 230–246, 1994. Available at http://www.lsv.ens-cachan.fr/Publis/PAPERS/APS-icci94.ps.
C. Autant and Ph. Schnoebelen. Place bisimulations in Petri nets. In Proc. 13th Int. Conf. Application and Theory of Petri Nets (ICATPN’92), Sheffield, UK, June 1992, volume 616 of Lecture Notes in Computer Science, pages 45–61. Springer, 1992.
G. Berthelot. Checking properties of nets using transformation. In Advances in Petri Nets 1985, volume 222 of Lecture Notes in Computer Science, pages 19–40. Springer, 1986.
R. Cleaveland, J. Parrow, and B. Steffen. The Concurrency Workbench: A semantics-based tool for the verification of concurrent systems. ACM Transactions on Programming Languages and Systems, 15(1):36–72, 1993.
R. J. van Glabbeek. The linear time — branching time spectrum. In Proc. Theories of Concurrency (CONCUR’90), Amsterdam, NL, Aug. 1990, volume 458 of Lecture Notes in Computer Science, pages 278–297. Springer, 1990.
P. Jančar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281–301, 1995.
R. Milner. Communication and Concurrency. Prentice Hall Int., 1989.
R. Milner. Operational and algebraic semantics of concurrent processes. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, vol. B, chapter 19, pages 1201–1242. Elsevier Science, 1990.
M. Nakagawa, S. Kumagai, T. Miyamoto, and D.-I. Lee. Equivalent net reduction for firing sequence preservation. IEICE Trans. on Fundamentals E., 78-A(11):1447–1457, 1995.
M. Nielsen and P. S. Thiagarajan. Degrees of non-determinism and concurrency: A Petri net view. In Proc. 4th Conf. Found. of Software Technology and Theor. Comp. Sci. (FST&TCS’84), Bangalore, India, Dec. 1984, volume 181 of Lecture Notes in Computer Science, pages 89–117. Springer, 1984.
E.-R. Olderog. Strong bisimilarity on nets: a new concept for comparing net semantics. In Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, Proc. REX School/Workshop, Noordwijkerhout, NL, May–June 1988, volume 354 of Lecture Notes in Computer Science, pages 549–573. Springer, 1989.
E.-R. Olderog. Nets, Terms and Formulas, volume 23 of Cambridge Tracts in Theoretical Computer Science. Cambridge Univ. Press, 1991.
D. Park. Concurrency and automata on infinite sequences. In Proc. 5th GI Conf. on Theor. Comp. Sci., Karlsruhe, FRG, Mar. 1981, volume 104 of Lecture Notes in Computer Science, pages 167–183. Springer, 1981.
L. Pomello. Some equivalence notions for concurrent systems. An overview. In Advances in Petri Nets 1985, volume 222 of Lecture Notes in Computer Science, pages 381–400. Springer, 1986.
W. Quivrin-Pfister. Des bisimulations de places pour la réduction des réseaux de Petri. Thèse de Doctorat, I.N.P. de Grenoble, France, November 1995.
S. M. Shatz, S. Tu, T. Murata, and S. Duri. An application of Petri net reduction for Ada tasking deadlock analysis. IEEE Trans. Parallel and Distributed Systems, 7(12):1309–1324, 1996.
M. Voorhoeve. Structural Petri net equivalence. Tech. report, Eindhoven Technical University, Dept. Computer Science, 1996. Available at ftp://ftp.win.tue.nl/pub/techreports/wsinmar/.
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Schnoebelen, P., Sidorova, N. (2000). Bisimulation and the Reduction of Petri Nets. In: Nielsen, M., Simpson, D. (eds) Application and Theory of Petri Nets 2000. ICATPN 2000. Lecture Notes in Computer Science, vol 1825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44988-4_23
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DOI: https://doi.org/10.1007/3-540-44988-4_23
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