Abstract
We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens.
We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abdulla, P.A., et al.: General decidability theorems for infinite-state systems. In: Proc. of LICS’96, pp. 313–321 (1996)
Abdulla, P.A., Delzanno, G.: On the Coverability Problem for Constrained Multiset Rewriting. In: Proc. of AVIS’06, Satellite workshop of ETAPS’06, Vienna, Austria (2006)
Abdulla, P.A., et al.: A Survey of Regular Model Checking. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, Springer, Heidelberg (2004)
Abdulla, P.A., Jonsson, B.: Verifying Networks of Timed Processes (Extended Abstract). In: Steffen, B. (ed.) ETAPS 1998 and TACAS 1998. LNCS, vol. 1384, pp. 298–312. Springer, Heidelberg (1998)
Annichini, A., Asarin, E., Bouajjani, A.: Symbolic techniques for parametric reasoning about counter and clock systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, Springer, Heidelberg (2000)
Arons, T., et al.: Parameterized Verification with Automatically Computed Inductive Assertions. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, Springer, Heidelberg (2001)
Boigelot, B.: Symbolic Methods for Exploring Infinite State Space. PhD thesis, Faculté des Sciences, Université de Liège, vol. 189 (1999)
Bojanczyk, M., et al.: Two-variable logic on data trees and XML reasoning. In: Proc. of PODS’06, ACM Press, New York (2006)
Bojanczyk, M., et al.: Two-variable logic on words with data. In: Proc. of LICS’06, IEEE Computer Society Press, Los Alamitos (2006)
Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem, 2nd edn. Universitext. Springer, Heidelberg (2001)
Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)
Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract Regular Model Checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, Springer, Heidelberg (2004)
Bouajjani, A., et al.: Regular Model Checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, Springer, Heidelberg (2000)
Bouajjani, A., Jurski, Y., Sighireanu, M.: A generic framework for reasoning about dynamic networks of infinite-state processes. Technical Report 2007-01, LIAFA lab (January 2007), Available at http://www.liafa.jussieu.fr/~abou/publis.html
Bouajjani, A., Müller-Olm, M., Touili, T.: Regular symbolic analysis of dynamic networks of pushdown systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, Springer, Heidelberg (2005)
Bouajjani, A., Touili, T.: On computing reachability sets of process rewrite systems. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, Springer, Heidelberg (2005)
Bouajjani, A.: Languages, Rewriting systems, and Verification of Infinte-State Systems. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, Springer, Heidelberg (2001)
Bozzano, M., Delzanno, G.: Beyond Parameterized Verification. In: Katoen, J.-P., Stevens, P. (eds.) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, Springer, Heidelberg (2002)
Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, Springer, Heidelberg (2005)
Clarke, E.M., Grumberg, O., Jha, S.: Verifying parameterized networks. TOPLASÂ 19(5) (1997)
Delzanno, G.: An assertional language for the verification of systems parametric in several dimensions. Electr. Notes Theor. Comput. Sci. 50(4) (2001)
Delzanno, G., Raskin, J.-F., Van Begin, L.: Towards the automated verification of multithreaded java programs. In: Katoen, J.-P., Stevens, P. (eds.) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, pp. 173–187. Springer, Heidelberg (2002)
Demri, S., Lazic, R.: LTL with the freeze quantifier and register automata. In: Proc. of LICS’06, IEEE Computer Society Press, Los Alamitos (2006)
Emerson, E.A., Namjoshi, K.S.: On model checking for non-deterministic infinite-state systems. In: LICS’98, IEEE Computer Society Press, Los Alamitos (1998)
Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: Proceedings of LICS ’99, pp. 352–359. IEEE Computer Society Press, Los Alamitos (1999)
Finkel, A., Leroux, J.: How to compose presburger-accelerations: Applications to broadcast protocols. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, Springer, Heidelberg (2002)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere? Theor. Comput. Sci. 256(1-2), 63–92 (2001)
Flanagan, C., Freund, S.N., Qadeer, S.: Thread-modular verification for shared-memory programs. In: Le Métayer, D. (ed.) ESOP 2002 and ETAPS 2002. LNCS, vol. 2305, pp. 262–277. Springer, Heidelberg (2002)
German, S.M., Sistla, P.A.: Reasoning about systems with many processes. JACMÂ 39(3) (1992)
Wolper, P., Boigelot, B.: Verifying systems with infinite but regular state spaces. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, Springer, Heidelberg (1998)
Wolper, P., Lovinfosse, V.: Verifying properties of large sets of processes with network invariants. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, Springer, Heidelberg (1990)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Bouajjani, A., Jurski, Y., Sighireanu, M. (2007). A Generic Framework for Reasoning About Dynamic Networks of Infinite-State Processes. In: Grumberg, O., Huth, M. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2007. Lecture Notes in Computer Science, vol 4424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71209-1_54
Download citation
DOI: https://doi.org/10.1007/978-3-540-71209-1_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71208-4
Online ISBN: 978-3-540-71209-1
eBook Packages: Computer ScienceComputer Science (R0)