Abstract
Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of the unfolding of a P/T Petri net contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.
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References
Abdulla, P.A., Iyer, S.P., Nylén, A.: Unfoldings of unbounded Petri nets. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 495–507. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_37
Best, E., Grahlmann, B.: Programming Environment based on Petri nets - Documentation and User Guide Version 1.4 (1995). https://uol.de/f/2/dept/informatik/ag/parsys/PEP1.4_man.ps.gz?v=1346500853
Chatain, T.: Symbolic unfoldings of high-level Petri nets and application to supervision of distributed systems, Ph. D. thesis, Universit é de Rennes (2006). https://www.sudoc.fr/246936924
Chatain, T., Fabre, E.: Factorization properties of symbolic unfoldings of colored Petri nets. In: Lilius, J., Penczek, W. (eds.) PETRI NETS 2010. LNCS, vol. 6128, pp. 165–184. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13675-7_11
Chatain, T., Jard, C.: Symbolic diagnosis of partially observable concurrent systems. In: de Frutos-Escrig, D., Núñez, M. (eds.) FORTE 2004. LNCS, vol. 3235, pp. 326–342. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30232-2_21
Chatain, T., Jard, C.: Complete finite prefixes of symbolic unfoldings of safe time Petri nets. In: Donatelli, S., Thiagarajan, P.S. (eds.) ICATPN 2006. LNCS, vol. 4024, pp. 125–145. Springer, Heidelberg (2006). https://doi.org/10.1007/11767589_8
Desel, J., Juhás, G., Neumair, C.: Finite unfoldings of unbounded Petri nets. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 157–176. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27793-4_10
Ehrig, H., Hoffmann, K., Padberg, J., Baldan, P., Heckel, R.: High-level net processes. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 191–219. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45711-9_12
Engelfriet, J.: Branching processes of Petri nets. Acta Informatica 28(6), 575–591 (1991). https://doi.org/10.1007/BF01463946
Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Formal Methods Syst. Des. 20(3), 285–310 (2002). https://doi.org/10.1023/A:1014746130920
Herbreteau, F., Sutre, G., Tran, T.Q.: Unfolding concurrent well-structured transition systems. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 706–720. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71209-1_55
Jensen, K.: Coloured Petri nets - basic concepts, analysis methods and practical use - volume 1, Second Edition. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (1996). https://doi.org/10.1007/978-3-662-03241-1
Khomenko, V., Koutny, M.: Branching processes of high-level Petri nets. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 458–472. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36577-X_34
McMillan, K.L.: A technique of state space search based on unfolding. Formal Methods Syst. Des. 6(1), 45–65 (1995). https://doi.org/10.1007/BF01384314
Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains, part I. Theor. Comput. Sci. 13, 85–108 (1981). https://doi.org/10.1016/0304-3975(81)90112-2
Presburger, M.: über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In: Proc. Comptes-rendus du I Congrés des Mathématiciens des Pays Slaves, Varsovie 1929, pp. 92–101 (1930)
Reisig, W.: Understanding petri nets - modeling techniques, analysis methods, case studies. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-33278-4
Würdemann, N., Chatain, T., Haar, S.: Taking complete finite prefixes to high level, symbolically (Full Version) (2023). https://hal.inria.fr/hal-04029490
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Würdemann, N., Chatain, T., Haar, S. (2023). Taking Complete Finite Prefixes to High Level, Symbolically. In: Gomes, L., Lorenz, R. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2023. Lecture Notes in Computer Science, vol 13929. Springer, Cham. https://doi.org/10.1007/978-3-031-33620-1_7
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