Abstract
Reachability analysis of pushdown systems is a fundamental problem in model checking that comes with a wide range of applications. We study performance improvements of pushdown reachability analysis and as a case study, we consider the verification of the policy-compliance of MPLS (Multiprotocol Label Switching) networks, an application domain that has recently received much attention. Our main contribution are three techniques that allow us to speed up the state-of-the-art pushdown reachability tools by an order of magnitude. These techniques include the combination of classic \( pre ^*\) and \( post ^*\) saturation algorithms into a dual-search algorithm, an on-the-fly technique for detecting the possibility of early termination, as well as a counter-example guided abstraction refinement technique that improves the performance in particular for the negative instances where the early termination technique is not applicable. As a second contribution, we describe an improved translation of MPLS networks to pushdown systems and demonstrate on an extensive set of benchmarks of real internet wide-area networks the efficiency of our approach.
Research supported by the Vienna Science and Technology Fund (WWTF), ICT19-045 (WHATIF), and the DFF project QASNET.
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
References
Anderson, C.J., et al.: NetKAT: semantic foundations for networks. In: POPL 2014, pp. 113–126. ACM (2014)
Beckett, R., Mahajan, R., Millstein, T., Padhye, J., Walker, D.: Don’t mind the gap: bridging network-wide objectives and device-level configurations. In: ACM SIGCOMM 2016, pp. 328–341. ACM (2016)
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). https://doi.org/10.1007/3-540-63141-0_10
Büchi, J.R.: Regular canonical systems. Archiv für mathematische Logik und Grundlagenforschung 6(3–4), 91–111 (1964)
Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_15
Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Prog. Lang. Syst. 16(5), 1512–1542 (1994)
Conway, C.L., Namjoshi, K.S., Dams, D., Edwards, S.A.: Incremental algorithms for inter-procedural analysis of safety properties. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 449–461. Springer, Heidelberg (2005). https://doi.org/10.1007/11513988_45
El-Hassany, A., Tsankov, P., Vanbever, L., Vechev, M.: Network-wide configuration synthesis. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 261–281. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_14
Esparza, J., Kiefer, S., Schwoon, S.: Abstraction refinement with Craig interpolation and symbolic pushdown systems. J. Satisf. Boolean Model. Comput. 5(1–4), 27–56 (2009)
Esparza, J., Knoop, J.: An automata-theoretic approach to interprocedural data-flow analysis. In: Thomas, W. (ed.) FoSSaCS 1999. LNCS, vol. 1578, pp. 14–30. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49019-1_2
Esparza, J., Schwoon, S.: A BDD-based model checker for recursive programs. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 324–336. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44585-4_30
Finkel, A., Willems, B., Wolper, P.: A direct symbolic approach to model checking pushdown systems. In: INFINITY 1997. ENTCS, vol. 9, pp. 27–37. Elsevier (1997)
Jensen, J.S., Krøgh, T.B., Madsen, J.S., Schmid, S., Srba, J., Thorgersen, M.T.: P-Rex: fast verification of MPLS networks with multiple link failures. In: CoNEXT, pp. 217–227. ACM (2018)
Jensen, P.G., Kristiansen, D., Schmid, S., Schou, M.K., Schrenk, B.C., Srba, J.: AalWiNes: a fast and quantitative what-if analysis tool for MPLS networks. In: CoNEXT 2020, pp. 474–481. ACM (2020)
Kazemian, P., Varghese, G., McKeown, N.: Header space analysis: static checking for networks. In: Proceedings of the NSDI, pp. 113–126 (2012)
Knight, S., Nguyen, H., Falkner, N., Bowden, R., Roughan, M.: The internet topology Zoo. IEEE J. Sel. Areas Commun. 29(9), 1765–1775 (2011)
Schmid, S., Srba, J.: Polynomial-time what-if analysis for prefix-manipulating MPLS networks. In: IEEE INFOCOM 2018, pp. 1799–1807. IEEE (2018)
Schwoon, S.: Model-checking pushdown systems. Ph.D. thesis, Technische Universität München (2002)
Schwoon, S.: Moped (2002). http://www2.informatik.uni-stuttgart.de/fmi/szs/tools/moped/
Suwimonteerabuth, D., Schwoon, S., Esparza, J.: jMoped: a java bytecode checker based on moped. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 541–545. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31980-1_35
Acknowledgements
We thank to Bernhard Schrenk for updating the AalWiNes online demo at https://demo.aalwines.cs.aau.dk with the improved verification engine described in this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Jensen, P.G., Schmid, S., Schou, M.K., Srba, J., Vanerio, J., Duijn, I.v. (2021). Faster Pushdown Reachability Analysis with Applications in Network Verification. In: Hou, Z., Ganesh, V. (eds) Automated Technology for Verification and Analysis. ATVA 2021. Lecture Notes in Computer Science(), vol 12971. Springer, Cham. https://doi.org/10.1007/978-3-030-88885-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-88885-5_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-88884-8
Online ISBN: 978-3-030-88885-5
eBook Packages: Computer ScienceComputer Science (R0)