Abstract
We consider the problem of efficiently computing models for satisfiable constraints, in the presence of complex background theories such as floating-point arithmetic. Model construction has various applications, for instance the automatic generation of test inputs. It is well-known that naive encoding of constraints into simpler theories (for instance, bit-vectors or propositional logic) can lead to a drastic increase in size, and be unsatisfactory in terms of memory and runtime needed for model construction. We define a framework for systematic application of approximations in order to speed up model construction. Our method is more general than previous techniques in the sense that approximations that are neither under- nor over-approximations can be used, and shows promising results in practice.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Boldo, S., Filliâtre, J.-C., Melquiond, G.: Combining Coq and Gappa for certifying floating-point programs. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds.) MKM 2009, Held as Part of CICM 2009. LNCS, vol. 5625, pp. 59–74. Springer, Heidelberg (2009)
Brain, M., D’Silva, V., Griggio, A., Haller, L., Kroening, D.: Deciding floating-point logic with abstract conflict driven clause learning. In: FMSD (2013)
Brillout, A., Kroening, D., Wahl, T.: Mixed abstractions for floating-point arithmetic. In: FMCAD. IEEE (2009)
Brummayer, R., Biere, A.: Effective bit-width and under-approximation. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2009. LNCS, vol. 5717, pp. 304–311. Springer, Heidelberg (2009)
Bryant, R.E., Kroening, D., Ouaknine, J., Seshia, S.A., Strichman, O., Brady, B.A.: Deciding bit-vector arithmetic with abstraction. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 358–372. Springer, Heidelberg (2007)
Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The MathSAT5 SMT solver. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 93–107. Springer, Heidelberg (2013)
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, Springer, Heidelberg (2000)
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)
Daumas, M., Melquiond, G.: Certification of bounds on expressions involving rounded operators. ACM Trans. Math. Softw. 37(1) (2010)
D’Silva, V., Haller, L., Kroening, D.: Abstract conflict driven learning. In: POPL. ACM (2013)
D’Silva, V., Haller, L., Kroening, D., Tautschnig, M.: Numeric bounds analysis with conflict-driven learning. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 48–63. Springer, Heidelberg (2012)
Gao, S., Kong, S., Clarke, E.M.: dReal: An SMT solver for nonlinear theories over the reals. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 208–214. Springer, Heidelberg (2013)
Ge, Y., de Moura, L.: Complete instantiation for quantified formulas in satisfiability modulo theories. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 306–320. Springer, Heidelberg (2009)
Giunchiglia, F., Walsh, T.: A theory of abstraction. Artif. Intell. 57(2-3) (1992)
Harrison, J.: Floating point verification in HOL Light: the exponential function. TR 428, University of Cambridge Computer Laboratory (1997), available on the Web as http://www.cl.cam.ac.uk/~jrh13/papers/tang.html
Harrison, J.: Handbook of Practical Logic and Automated Reasoning. Cambridge University Press (2009)
IEEE Comp. Soc.: IEEE Standard for Floating-Point Arithmetic 754-2008 (2008)
Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 114–128. Springer, Heidelberg (2012)
Khanh, T.V., Ogawa, M.: SMT for polynomial constraints on real numbers. In: TAPAS. Electronic Notes in Theoretical Computer Science, vol. 289 (2012)
Lapschies, F., Peleska, J., Gorbachuk, E., Mangels, T.: SONOLAR SMT-solver. In: Satisfiability Modulo Theories Competition; System Description (2012)
Melquiond, G.: Floating-point arithmetic in the Coq system. In: Conf. on Real Numbers and Computers. Information & Computation, vol. 216. Elsevier (2012)
de Moura, L., Bjørner, N.S.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
de Moura, L., Passmore, G.O.: The strategy challenge in SMT solving. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated Reasoning and Mathematics. LNCS, vol. 7788, pp. 15–44. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Zeljić, A., Wintersteiger, C.M., Rümmer, P. (2014). Approximations for Model Construction. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-08587-6_26
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08586-9
Online ISBN: 978-3-319-08587-6
eBook Packages: Computer ScienceComputer Science (R0)