Abstract
We are interested in automatically proving safety properties of infinite state systems. We present a technique for invariant synthesis which can be incorporated in backward reachability analysis. The main theoretical result ensures that (under suitable hypotheses) our method is guaranteed to find an invariant if one exists. We also discuss heuristics that allow us to derive an implementation of the technique showing remarkable speed-ups on a significant set of safety problems in parametrised systems.
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References
Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: Proc. of LICS, pp. 313–321 (1996)
Abdulla, P.A., Delzanno, G., Ben Henda, N., Rezine, A.: Regular model checking without transducers (On efficient verification of parameterized systems). In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 721–736. Springer, Heidelberg (2007)
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)
Beyer, D., Henzinger, T.A., 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)
Bradley, A.R., Manna, Z.: Property-Directed Incremental Invariant Generation. Formal Aspects of Computing (to appear, 2009)
Delzanno, G., Esparza, J., Podelski, A.: Constraint-based analysis of broadcast protocols. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 50–66. Springer, Heidelberg (1999)
Enderton, H.B.: A Mathematical Introduction to Logic. Academic Press, New York (1972)
Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: Proc. of LICS, pp. 352–359. IEEE Computer Society Press, Los Alamitos (1999)
Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: Proc. of POPL 2002, pp. 191–202. ACM Press, New York (2002)
Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Towards SMT Model Checking of Array-Based Systems. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195, pp. 67–82. Springer, Heidelberg (2008)
Ghilardi, S., Ranise, S.: Goal-directed Invariant Synthesis for Model Checking Modulo Theories. Technical Report RI325-09, Univ. di Milano (2009)
Ghilardi, S., Ranise, S., Valsecchi, T.: Light-Weight SMT-based Model-Checking. In: Proc. of AVOCS 2007-2008. ENTCS (2008)
Lahiri, S.K., Bryant, R.E.: Predicate Abstraction with Indexed Predicate. ACM Trans. on Comp. Logic 9(1) (2007)
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)
Pnueli, A., Ruah, S., Zuck, L.D.: Automatic deductive verification with invisible invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001)
Ranise, S., Tinelli, C.: The SMT-LIB Standard: Version 1.2. Technical report, Dep. of Comp. Science, Iowa (2006), http://www.SMT-LIB.org/papers
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Ghilardi, S., Ranise, S. (2009). Goal-Directed Invariant Synthesis for Model Checking Modulo Theories . In: Giese, M., Waaler, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science(), vol 5607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02716-1_14
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DOI: https://doi.org/10.1007/978-3-642-02716-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02715-4
Online ISBN: 978-3-642-02716-1
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