Abstract
One approach for smt solvers to improve efficiency is to delegate reasoning to abstract domains. Solvers using abstract domains do not support interpolation and cannot be used for interpolation-based verification. We extend Abstract Conflict Driven Clause Learning (acdcl) solvers with proof generation and interpolation. Our results lead to the first interpolation procedure for floating-point logic and subsequently, the first interpolation-based verifiers for programs with floating-point variables. We demonstrate the potential of this approach by verifying a number of programs which are challenging for current verification tools.
Supported by the Toyota Motor Corporation, ERC project 280053, EPSRC project EP/J012564/1, and the FP7 STREP PINCETTE.
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References
Brain, M., D’Silva, V., Haller, L., Griggio, A., Kroening, D.: An abstract interpretation of DPLL(T). In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 455–475. Springer, Heidelberg (2013)
Brillout, A., Kroening, D., Wahl, T.: Mixed abstractions for floating-point arithmetic. In: Proc. of Formal Methods in Computer-Aided Design, pp. 69–76. IEEE Computer Society Press (2009)
Cimatti, A., Griggio, A.: Software model checking via IC3. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 277–293. Springer, Heidelberg (2012)
Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The mathSAT5 SMT solver. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 93–107. Springer, Heidelberg (2013)
Cimatti, A., Griggio, A., Sebastiani, R.: Efficient generation of Craig interpolants in satisfiability modulo theories. ACM Transactions on Computational Logic 12(1), 7 (2010)
Clarke, E.M., Kroening, D., Sharygina, N., Yorav, K.: Predicate abstraction of ANSI-C programs using SAT. Formal Methods in Systems Design 25(2-3), 105–127 (2004)
Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: The ASTREÉ analyzer. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 21–30. Springer, Heidelberg (2005)
Delmas, D., Goubault, E., Putot, S., Souyris, J., Tekkal, K., Védrine, F.: Towards an industrial use of FLUCTUAT on safety-critical avionics software. In: Alpuente, M., Cook, B., Joubert, C. (eds.) FMICS 2009. LNCS, vol. 5825, pp. 53–69. Springer, Heidelberg (2009)
D’Silva, V., Haller, L., Kroening, D.: Abstract conflict driven learning. In: Proc. of Principles of Programming Languages, pp. 143–154 (2013)
D’Silva, V., Haller, L., Kroening, D., Tautschnig, M.: Numeric bounds analysis with conflict-driven learning. In: Proc. of Tools and Algorithms for the Construction and Analysis of Systems, pp. 48–63 (2012)
Garoche, P.-L., Kahsai, T., Tinelli, C.: Invariant stream generators using automatic abstract transformers based on a decidable logic. CoRR, abs/1205.3758 (2012)
Griggio, A.: Effective word-level interpolation for software verification. In: Proc. of Formal Methods in Computer-Aided Design (2011)
Gulavani, B.S., Chakraborty, S., Nori, A.V., Rajamani, S.K.: Automatically refining abstract interpretations. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 443–458. Springer, Heidelberg (2008)
Haller, L., Griggio, A., Brain, M., Kroening, D.: Deciding floating-point logic with systematic abstraction. In: Proc. of Formal Methods in Computer-Aided Design, pp. 131–140 (2012)
Kovács, L., Voronkov, A.: Interpolation and symbol elimination. In: Schmidt, R.A. (ed.) CADE 2009. LNCS, vol. 5663, pp. 199–213. Springer, Heidelberg (2009)
Kroening, D., Weissenbacher, G.: Lifting propositional interpolants to the word-level. In: FMCAD, pp. 85–89. IEEE (2007)
Kroening, D., Weissenbacher, G.: Interpolation-based software verification with Wolverine. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 573–578. Springer, Heidelberg (2011)
McMillan, K.L.: Interpolation and SAT-based model checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)
McMillan, K.L.: An interpolating theorem prover. Theoretical Computer Science 345(1), 101–121 (2005)
McMillan, K.L.: Lazy abstraction with interpolants. In: LPAR-18 2012, pp. 123–136. Springer (2006)
Muller, J.-M., Brisebarre, N., de Dinechin, F., Jeannerod, C.-P., Lefèvre, V., Melquiond, G., Revol, N., Stehlé, D., Torres, S.: Handbook of Floating-Point Arithmetic. Birkhäuser, Boston (2010)
Ponsini, O., Michel, C., Rueher, M.: Refining abstract interpretation based value analysis with constraint programming techniques. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 593–607. Springer, Heidelberg (2012)
Totla, N., Wies, T.: Complete instantiation-based interpolation. In: Proc. of Principles of Programming Languages, pp. 537–548. ACM Press (2013)
Truchet, C., Pelleau, M., Benhamou, F.: Abstract domains for constraint programming, with the example of octagons. In: Symbolic and Numeric Algorithms for Scientific Computing, pp. 72–79 (2010)
Zhang, L., Malik, S.: The quest for efficient Boolean satisfiability solvers. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 295–313. Springer, Heidelberg (2002)
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Brain, M., D’Silva, V., Griggio, A., Haller, L., Kroening, D. (2013). Interpolation-Based Verification of Floating-Point Programs with Abstract CDCL. In: Logozzo, F., Fähndrich, M. (eds) Static Analysis. SAS 2013. Lecture Notes in Computer Science, vol 7935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38856-9_22
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