Abstract
In recent years, a research thread focused on the use of the unfolding semantics for verification purposes. This started with a paper by McMillan, which devises an algorithm for constructing a finite complete prefix of the unfolding of a safe Petri net, providing a compact representation of the reachability graph. The extension to contextual nets and graph transformation systems is far from being trivial because events can have multiple causal histories. Recently, we proposed an abstract algorithm that generalizes McMillan’s construction to bounded contextual nets without resorting to an encoding into plain P/T nets. Here, we provide a more explicit construction that renders the algorithm effective. To allow for an inductive definition of concurrency, missing in the original proposal and essential for an efficient unfolding procedure, the key intuition is to associate histories not only with events, but also with places. Additionally, we outline how the proposed algorithm can be extended to graph transformation systems, for which previous algorithms based on the encoding of read arcs would not be applicable.
Supported by the MIUR Project SisteR, by the project AVIAMO of the University of Padova and by the DFG project SANDS.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baldan, P., Chatain, T., Haar, S., König, B.: Unfolding-based diagnosis of systems with an evolving topology. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 203–217. Springer, Heidelberg (2008)
Baldan, P., Corradini, A., König, B.: Verifying finite-state graph grammars: an unfolding-based approach. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 83–98. Springer, Heidelberg (2004)
Baldan, P., Corradini, A., König, B., Schwoon, S.: McMillan’s complete prefix for contextual nets. In: Jensen, K., van der Aalst, W.M.P., Billington, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency I. LNCS, vol. 5100, pp. 199–220. Springer, Heidelberg (2008)
Baldan, P., Corradini, A., Montanari, U.: An event structure semantics for P/T contextual nets: Asymmetric event structures. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 63–80. Springer, Heidelberg (1998)
Baldan, P., Corradini, A., Montanari, U., Ribeiro, L.: Unfolding Semantics of Graph Transformation. Information and Computation 205, 733–782 (2007)
Baldan, P., Corradini, A., Heindel, T., König, B., Sobociński, P.: Unfolding grammars in adhesive categories. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 350–366. Springer, Heidelberg (2009)
Benveniste, A., Haar, S., Fabre, E., Jard, C.: Distributed monitoring of concurrent and asynchronous systems. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 1–26. Springer, Heidelberg (2003)
Bonet, B., Haslum, P., Hickmott, S.L., Thiébaux, S.: Directed unfolding of Petri nets. In: Jensen, K., van der Aalst, W.M.P., Billington, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency I. LNCS, vol. 5100, pp. 172–198. Springer, Heidelberg (2008)
Langerak, R.: Transformation and Semantics for LOTOS. Ph.D. thesis, Department of Computer Science, University of Twente (1992)
McMillan, K.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–174. Springer, Heidelberg (1993)
McMillan, K.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)
Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85–108 (1981)
Pinna, G.M., Poigné, A.: On the nature of events: another perspective in concurrency. Theoretical Computer Science 138(2), 425–454 (1995)
Vogler, W., Semenov, A., Yakovlev, A.: Unfolding and finite prefix for nets with read arcs. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 501–516. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baldan, P., Bruni, A., Corradini, A., König, B., Schwoon, S. (2010). On the Computation of McMillan’s Prefix for Contextual Nets and Graph Grammars. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds) Graph Transformations. ICGT 2010. Lecture Notes in Computer Science, vol 6372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15928-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-15928-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15927-5
Online ISBN: 978-3-642-15928-2
eBook Packages: Computer ScienceComputer Science (R0)