Abstract
We study certain classes of verification problems for parametric reactive and hybrid systems, and identify the types of logical theories which can be used for modeling such systems and the reasoning tasks which need to be solved in this context. We identify properties of the underlying theories which ensure that these classes of verification problems can be solved efficiently, give examples of theories with the desired properties, and illustrate the methods we use on several examples.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A., Ho, P.H.: Automatic Symbolic Verification of Embedded Systems. IEEE Trans. Software Eng. 22(3), 181–201 (1996)
Beyer, D., Henzinger, T., Majumdar, R., Rybalchenko, A.: Invariant Synthesis for Combined Theories. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 378–394. Springer, Heidelberg (2007)
Cimatti, A., Palopoli, L., Ramadian, Y.: Symbolic Computation of Schedulability Regions Using Parametric Timed Automata. In: IEEE Real-Time Systems Symposium 2008, pp. 80–89. IEEE Computer Society, Los Alamitos (2008)
Cimatti, A., Roveri, M., Tonetta, S.: Requirements Validation for Hybrid Systems. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 188–203. Springer, Heidelberg (2009)
Dolzmann, A., Sturm, T.: Redlog: Computer Algebra Meets Computer Logic. ACM SIGSAM Bulletin 31(2), 2–9 (1997)
Frehse, G., Jha, S.K., Krogh, B.H.: A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 187–200. Springer, Heidelberg (2008)
Ganzinger, H., Sofronie-Stokkermans, V., Waldmann, U.: Modular proof systems for partial functions with Evans equality. Information and Computation 204(10), 1453–1492 (2006)
Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 362–378. Springer, Heidelberg (2007)
Gulwani, S., Tiwari, A.: Constraint-Based Approach for Analysis of Hybrid Systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190–203. Springer, Heidelberg (2008)
Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.: Linear Parametric Model Checking of Timed Automata. Journal of Logic and Algebraic Programming 52-53, 183–220 (2002)
Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On Local Reasoning in Verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008)
Ihlemann, C., Sofronie-Stokkermans, V.: On Hierarchical Reasoning in Combinations of Theories. In: Giesl, J., Hähnle, R. (eds.) Proceedings of IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 30–45. Springer, Heidelberg (2010)
Jacobs, S., Sofronie-Stokkermans, V.: Applications of Hierarchical Reasoning in the Verification of Complex Systems. Electr. Notes Theor. Comput. Sci. 174(8), 39–54 (2007)
Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, Heidelberg (1995)
Platzer, A., Quesel, J.-D.: European Train Control System: A Case Study in Formal Verification. In: Cavalcanti, A. (ed.) ICFEM 2009. LNCS, vol. 5885, pp. 246–265. Springer, Heidelberg (2009)
Sofronie-Stokkermans, V.: Hierarchic Reasoning in Local Theory Extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 219–234. Springer, Heidelberg (2005)
Sofronie-Stokkermans, V., Ihlemann, C.: Automated Reasoning in some Local Extensions of Ordered Structures. Journal of Multiple-Valued Logics and Soft Computing 13(4-6), 397–414 (2007)
Sofronie-Stokkermans, V.: Efficient Hierarchical Reasoning about Functions over Numerical Domains. In: Dengel, A.R., Berns, K., Breuel, T.M., Bomarius, F., Roth-Berghofer, T.R. (eds.) KI 2008. LNCS (LNAI), vol. 5243, pp. 135–143. Springer, Heidelberg (2008)
Tarski, A.: A Decision Method for Elementary Algebra and Geometry, 2nd edn. University of California Press, Berkeley (1951)
Wang, F.: Symbolic Parametric Safety Analysis of Linear Hybrid Systems with BDD-Like Data-Structures. IEEE Trans. Software Eng. 31(1), 38–51 (2005)
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
Sofronie-Stokkermans, V. (2010). Hierarchical Reasoning for the Verification of Parametric Systems. In: Giesl, J., Hähnle, R. (eds) Automated Reasoning. IJCAR 2010. Lecture Notes in Computer Science(), vol 6173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14203-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-14203-1_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14202-4
Online ISBN: 978-3-642-14203-1
eBook Packages: Computer ScienceComputer Science (R0)