Abstract
Lazy abstraction with interpolants has been shown to be a powerful technique for verifying imperative programs. In presence of arrays, however, the method shows an intrinsic limitation, due to the fact that successful invariants usually contain universally quantified variables, which are not present in the program specification. In this work we present an extension of the interpolation-based lazy abstraction in which arrays of unknown length can be handled in a natural manner. In particular, we exploit the Model Checking Modulo Theories framework, to derive a backward reachability version of lazy abstraction that embeds array reasoning. The approach is generic, in that it is valid for both parameterized systems and imperative programs. We show by means of experiments that our approach can synthesize and prove universally quantified properties over arrays in a completely automatic fashion.
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References
Alberti, F., Bruttomesso, R., Ghilardi, S., Ranise, S., Sharygina, N.: Lazy Abstraction with Interpolants for Arrays. extended version, http://homes.dsi.unimi.it/~ghilardi/allegati/ABGRS_LPAR.pdf
Brillout, A., Kroening, D., Rümmer, P., Wahl, T.: An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 384–399. Springer, Heidelberg (2010)
Carioni, A., Ghilardi, S., Ranise, S.: Automated Termination in Model Checking Modulo Theories. In: Delzanno, G., Potapov, I. (eds.) RP 2011. LNCS, vol. 6945, pp. 110–124. Springer, Heidelberg (2011)
Clarke, E.M., 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)
Cousot, P., Cousot, R., Logozzo, F.: A Parametric Segmentation Functor for Fully Automatic and Scalable Array Content Analysis. In: POPL (2011)
Dillig, I., Dillig, T., Aiken, A.: Fluid Updates: Beyond Strong vs. Weak Updates. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 246–266. Springer, Heidelberg (2010)
Dimitrova, R., Podelski, A.: Is Lazy Abstraction a Decision Procedure for Broadcast Protocols? In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 98–111. Springer, Heidelberg (2008)
Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: POPL, pp. 191–202 (2002)
Ghilardi, S., Ranise, S.: Model Checking Modulo Theory at work: the integration of Yices in MCMT. In: AFM (2009)
Ghilardi, S., Ranise, S.: Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis. LMCS 6(4) (2010)
Ghilardi, S., Ranise, S.: MCMT: A Model Checker Modulo Theories. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 22–29. Springer, Heidelberg (2010)
Gopan, D., Reps, T., Sagiv, M.: A Framework for Numeric Analysis of Array Operations. In: POPL 2005, pp. 338–350 (2005)
Graf, S., Saïdi, H.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)
Halbwachs, N., Mathias, P.: Discovering Properties about Arrays in Simple Programs. In: PLDI 2008, pp. 339–348 (2008)
Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from Proofs. In: POPL, pp. 232–244 (2004)
Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy Abstraction. In: POPL, pp. 58–70 (2002)
Jhala, R., McMillan, K.L.: Array Abstractions from Proofs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 193–206. Springer, Heidelberg (2007)
Kapur, D., Majumdar, R., Zarba, C.: Interpolation for Data Structures. In: SIGSOFT 2006/FSE-14, pp. 105–116 (2006)
Kovács, L., Voronkov, A.: Interpolation and Symbol Elimination. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 199–213. Springer, Heidelberg (2009)
McMillan, K.L.: Quantified Invariant Generation Using an Interpolating Saturation Prover. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 413–427. Springer, Heidelberg (2008)
McMillan, K.L.: Lazy Abstraction with Interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)
Ranise, S., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB) (2006), http://www.SMT-LIB.org
Seghir, M.N., Podelski, A., Wies, T.: Abstraction Refinement for Quantified Array Assertions. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 3–18. Springer, Heidelberg (2009)
Lahiri, S., Bryant, R.: Predicate Abstraction with Indexed Predicates. TOCL 9(1) (2007)
Srivastava, S., Gulwani, S.: Program Verification using Templates over Predicate Abstraction. In: PLDI (2009)
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Alberti, F., Bruttomesso, R., Ghilardi, S., Ranise, S., Sharygina, N. (2012). Lazy Abstraction with Interpolants for Arrays. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_7
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