Abstract
In this paper we introduce a new (non-Turing powerful) formal model of recursive concurrent programs called well-formed communicating recursive state machines (CRSM). CRSM extend recursive state machines (RSM) by allowing a restricted form of concurrency: a state of a module can be refined into a finite collection of modules (working in parallel) in a potentially recursive manner. Communication is only possible between the activations of modules invoked on the same fork. We study the model checking problem of CRSM with respect to specifications expressed in a temporal logic that extends CaRet with a parallel operator (ConCaRet). We propose a decision algorithm that runs in time exponential in both the size of the formula and the maximum number of modules that can be invoked simultaneously. This matches the known lower bound for deciding CaRet model checking of RSM, and therefore, we prove that model checking CRSM with respect to ConCaRet specifications is Exptime-complete.
This research was partially supported by the MIUR grant ex-60% 2003-2004 Università degli Studi di Salerno.
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
Alur, R., Benedikt, M., Etessami, K., Godefroid, P., Reps, T., Yannakakis, M.: Analysis of recursive state machines. To appear in ACM Transactions on Programming Languages and Systems (2005)
Alur, R., Etessami, K., Madhusudan, P.: A Temporal Logic of Nested Calls and Returns. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 467–481. Springer, Heidelberg (2004)
Alur, R., Kannan, S., Yannakakis, M.: Communicating hierarchical state machines. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 169–178. Springer, Heidelberg (1999)
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., Esparza, J., Touili, T.: A generic approach to the static analysis of concurrent programs with procedures. In: Proc. of POPL 2003, pp. 62–73 (2003)
Bouajjani, A., Touili, T.: Reachability Analysis of Process Rewrite Systems. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 74–87. Springer, Heidelberg (2003)
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, pp. 473–487. Springer, Heidelberg (2005)
Brainerd, W.S.: Tree generating regular systems. Information and Control 14, 217–231 (1969)
Esparza, J., Nielsen, M.: Decidability Issues for Petri Nets. J. Inform. Process. Cybernet. EIK 30(3), 143–160 (1994)
Esparza, J., Knoop, J.: An automata-theoretic approach to interprocedural parallel flow graphs. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 14–30. Springer, Heidelberg (1999)
Esparza, J., Podelski, A.: Efficient Algorithms for pre* and post* on Interprocedural Parallel Flow Graphs. In: Proc. of POPL 2000, pp. 1–11 (2000)
Löding, C.: Infinite Graphs Generated by Tree Rewriting. Doctoral thesis, RWTH Aachen (2003)
Mayr, R.: Process Rewrite Systems. Information and Computation 156, 264–286 (2000)
Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005)
Thomas, W.: Automata on infinite objets. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 133–191 (1990)
Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logics of programs. Journal of Computer and System Science 32(2), 183–221 (1986)
Walukiewicz, I.: Pushdown processes: Games and Model Checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996)
http://www.dia.unisa.it/professori/latorre/Papers/concaret.ps.gz
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bozzelli, L., La Torre, S., Peron, A. (2005). Verification of Well-Formed Communicating Recursive State Machines. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_27
Download citation
DOI: https://doi.org/10.1007/11609773_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31139-3
Online ISBN: 978-3-540-31622-0
eBook Packages: Computer ScienceComputer Science (R0)