Abstract
Under maximal semantics, the occurrence of an event \(a\) in a concurrent run of an occurrence net may imply the occurrence of other events, not causally related to \(a\), in the same run. In recent works, we have formalized this phenomenon as the reveals relation, and used it to obtain a contraction of sets of events called facets in the context of occurrence nets. Here, we extend this idea to propose a canonical contraction of general safe Petri nets into pieces of partial-order behaviour which can be seen as “macro-transitions” since all their events must occur together in maximal semantics. On occurrence nets, our construction coincides with the facets abstraction.Our contraction preserves the maximal semantics in the sense that the maximal processes of the contracted net are in bijection with those of the original net.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Notice that \((B, E, F, {^{\bullet }{E'}} \setminus {{E'}^{\bullet }})\) is not an occurrence net in general: it satisfies items 3, 4 and 5 of Definition 2, but items 1 and 2 may not hold.
- 2.
The depth of an event \(e\) is the size of the longest path from an initial condition to \(e\).
- 3.
By “\(\phi \) starts by \(t\)”, we mean that there exists an event in \(\phi \) which is mapped to \(t\) and consumes only initial conditions of \(\phi \).
References
Balaguer, S., Chatain, T., Haar, S.: Building tight occurrence nets from reveals relations. In: Proceedings of the 11th International Conference on Application of Concurrency to System Design, pp. 44–53. IEEE Computer Society Press (2011)
Balaguer, S., Chatain, T., Haar, S.: Building occurrence nets from reveals relations. Fundam. Inform. 123(3), 245–272 (2013)
Berthelot, G.: Checking properties of nets using transformation. In: Rozenberg, G. (ed.) APN 1985. LNCS, vol. 222, pp. 19–40. Springer, Heidelberg (1986)
Best, E., Randell, B.: A formal model of atomicity in asynchronous systems. Acta Inform. 16(1), 93–124 (1981)
Desel, J., Merceron, A.: Vicinity respecting homomorphisms for abstracting system requirements. In: Proceedings of International Workshop on Abstractions for Petri Nets and Other Models of Concurrency (APNOC) (2009)
Haar, S.: Types of asynchronous diagnosability and the reveals-relation in occurrence nets. IEEE Trans. Autom. Control 55(10), 2310–2320 (2010)
Haar, S., Kern, C., Schwoon, S.: Computing the reveals relation in occurrence nets. In: Proceedings of GandALF’11. Electronic Proceedings in Theoretical Computer Science, vol. 54, pp. 31–44 (2011)
Kumar, R., Takai, S.: Decentralized prognosis of failures in discrete event systems. IEEE Trans. Autom. Control 55(1), 48–59 (2010)
Madalinski, A., Khomenko, V.: Diagnosability verification with parallel LTL-X model checking based on Petri net unfoldings. In: Control and Fault-Tolerant Systems (SysTol’2010), pp. 398–403. IEEE Computing Society Press (2010)
Madalinski, A., Khomenko, V.: Predictability verification with parallel LTL-X model checking based on Petri net unfoldings. In: Proceedings of the 8th IFAC Symposium on Fault Detection, Diagnosis and Safety of Technical Processes (SAFEPROCESS’2012), pp. 1232–1237 (2012)
Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains, part I. Theoret. Comput. Sci. 13, 85–108 (1981)
Zielonka, W.: Notes on finite asynchronous automata. RAIRO Theoret. Inform. Appl. 21, 99–135 (1987)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chatain, T., Haar, S. (2014). A Canonical Contraction for Safe Petri Nets. In: Koutny, M., Haddad, S., Yakovlev, A. (eds) Transactions on Petri Nets and Other Models of Concurrency IX. Lecture Notes in Computer Science(), vol 8910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45730-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-45730-6_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45729-0
Online ISBN: 978-3-662-45730-6
eBook Packages: Computer ScienceComputer Science (R0)