Abstract
Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by trees and sets of states by tree automata. The central problem is to decide whether a set of bad states belongs to the set of reachable states. An obstacle is that this set is in general neither regular nor computable in finite time.
This paper proposes a new CounterExample Guided Abstraction Refinement (CEGAR) algorithm for TRMC. Our approach relies on a new equational-abstraction based completion algorithm to compute a regular overapproximation of the set of reachable states in finite time. This set is represented by \(\mathcal{R}_{/E}\)-automata, a new extended tree automaton formalism whose structure can be exploited to detect and remove false positives in an efficient manner. Our approach has been implemented in TimbukCEGAR, a new toolset that is capable of analyzing Java programs by exploiting an elegant translation from the Java byte code to term rewriting systems. Experiments show that TimbukCEGAR outperforms existing CEGAR-based completion algorithms. Contrary to existing TRMC toolsets, the answers provided by TimbukCEGAR are certified by Coq, which means that they are formally proved correct.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abdulla, P.A., Chen, Y.-F., Delzanno, G., Haziza, F., Hong, C.-D., Rezine, A.: Constrained Monotonic Abstraction: A CEGAR for Parameterized Verification. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 86–101. Springer, Heidelberg (2010)
Abdulla, P.A., Delzanno, G., Rezine, A.: Parameterized Verification of Infinite-State Processes with Global Conditions. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 145–157. Springer, Heidelberg (2007)
Abdulla, P.A., Ben Henda, N., Delzanno, G., Haziza, F., Rezine, A.: Parameterized Tree Systems. In: Suzuki, K., Higashino, T., Yasumoto, K., El-Fakih, K. (eds.) FORTE 2008. LNCS, vol. 5048, pp. 69–83. Springer, Heidelberg (2008)
Abdulla, P.A., Legay, A., d’Orso, J., Rezine, A.: Simulation-Based Iteration of Tree Transducers. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 30–44. Springer, Heidelberg (2005)
Avispa – a tool for Automated Validation of Internet Security Protocols, http://www.avispa-project.org
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)
Ball, T., Cook, B., Levin, V., Rajamani, S.K.: SLAM and Static Driver Verifier: Technology Transfer of Formal Methods inside Microsoft. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 1–20. Springer, Heidelberg (2004)
Barré, N., Besson, F., Genet, T., Hubert, L., Le Roux, L.: Copster homepage (2009), http://www.irisa.fr/celtique/genet/copster
Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. Springer (2004)
Boichut, Y., Boyer, B., Genet, T., Legay, A.: Fast Equational Abstraction Refinement for Regular Tree Model Checking. Technical report, INRIA (2010), http://hal.inria.fr/inria-00501487
Boichut, Y., Courbis, R., Héam, P.-C., Kouchnarenko, O.: Finer Is Better: Abstraction Refinement for Rewriting Approximations. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 48–62. Springer, Heidelberg (2008)
Boichut, Y., Dao, T.-B.-H., Murat, V.: Characterizing Conclusive Approximations by Logical Formulae. In: Delzanno, G., Potapov, I. (eds.) RP 2011. LNCS, vol. 6945, pp. 72–84. Springer, Heidelberg (2011)
Boichut, Y., Genet, T., Jensen, T., Le Roux, L.: Rewriting Approximations for Fast Prototyping of Static Analyzers. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 48–62. Springer, Heidelberg (2007)
Boigelot, B., Legay, A., Wolper, P.: Iterating Transducers in the Large (Extended Abstract). In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 223–235. Springer, Heidelberg (2003)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract regular tree model checking. ENTCS 149(1), 37–48 (2006)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract Regular Tree Model Checking of Complex Dynamic Data Structures. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 52–70. Springer, Heidelberg (2006)
Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract Regular Model Checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 372–386. Springer, Heidelberg (2004)
Bouajjani, A., Jonsson, B., Nilsson, M., Touili, T.: Regular Model Checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 403–418. Springer, Heidelberg (2000)
Bouajjani, A., Touili, T.: Extrapolating Tree Transformations. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 539–554. Springer, Heidelberg (2002)
Boyer, B., Genet, T., Jensen, T.: Certifying a Tree Automata Completion Checker. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 523–538. Springer, Heidelberg (2008)
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Löding, C., Tison, S., Tommasi, M.: Tree automata techniques and applications (2008)
Dams, D., Lakhnech, Y., Steffen, M.: Iterating transducers. Journal of Logic and Algebraic Programming (JLAP) 52-53, 109–127 (2002)
Feuillade, G., Genet, T., Viet Triem Tong, V.: Reachability Analysis over Term Rewriting Systems. Journal of Automated Reasonning 33(3-4), 341–383 (2004)
Genet, T.: Decidable Approximations of Sets of Descendants and Sets of Normal Forms. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 151–165. Springer, Heidelberg (1998)
Genet, T.: Reachability analysis of rewriting for software verification. Université de Rennes 1, Habilitation (2009)
Genet, T., Klay, F.: Rewriting for Cryptographic Protocol Verification. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 271–290. Springer, Heidelberg (2000)
Genet, T., Rusu, R.: Equational tree automata completion. JSC 45 (2010)
Genet, T., Tang-Talpin, Y.-M., Viet Triem Tong, V.: Verification of Copy Protection Cryptographic Protocol using Approximations of Term Rewriting Systems. In: WITS 2003 (2003)
Genet, T., Viet Triem Tong, V.: Timbuk 2.0 – a Tree Automata Library. IRISA/Université de Rennes 1 (2001), http://www.irisa.fr/celtique/genet/timbuk/
Gilleron, R., Tison, S.: Regular tree languages and rewrite systems. Fundamenta Informaticae 24, 157–175 (1995)
Kesten, Y., Maler, O., Marcus, M., Pnueli, A., Shahar, E.: Symbolic Model Checking with Rich Assertional Languages. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 424–435. Springer, Heidelberg (1997)
Lind-Nielsen, J.: Buddy 2.4 (2002), http://buddy.sourceforge.net
Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational abstractions. TCS 403, 239–264 (2008)
Patin, G., Sighireanu, M., Touili, T.: Spade: Verification of Multithreaded Dynamic and Recursive Programs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 254–257. Springer, Heidelberg (2007)
Podelski, A., Rybalchenko, A.: ARMC: The Logical Choice for Software Model Checking with Abstraction Refinement. In: Hanus, M. (ed.) PADL 2007. LNCS, vol. 4354, pp. 245–259. Springer, Heidelberg (2007)
Ravaj: Rewriting and Approximations for Java Applications Verification, http://www.irisa.fr/celtique/genet/RAVAJ
Takai, T.: A Verification Technique Using Term Rewriting Systems and Abstract Interpretation. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 119–133. Springer, Heidelberg (2004)
Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Using Language Inference to Verify Omega-Regular Properties. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 45–60. Springer, Heidelberg (2005)
Vardhan, A., Viswanathan, M.: LEVER: A Tool for Learning Based Verification. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 471–474. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boichut, Y., Boyer, B., Genet, T., Legay, A. (2012). Equational Abstraction Refinement for Certified Tree Regular Model Checking. In: Aoki, T., Taguchi, K. (eds) Formal Methods and Software Engineering. ICFEM 2012. Lecture Notes in Computer Science, vol 7635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34281-3_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-34281-3_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34280-6
Online ISBN: 978-3-642-34281-3
eBook Packages: Computer ScienceComputer Science (R0)