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Approximations for Model Construction

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Automated Reasoning (IJCAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

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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.

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References

  1. 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)

    Chapter  Google Scholar 

  2. Brain, M., D’Silva, V., Griggio, A., Haller, L., Kroening, D.: Deciding floating-point logic with abstract conflict driven clause learning. In: FMSD (2013)

    Google Scholar 

  3. Brillout, A., Kroening, D., Wahl, T.: Mixed abstractions for floating-point arithmetic. In: FMCAD. IEEE (2009)

    Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Daumas, M., Melquiond, G.: Certification of bounds on expressions involving rounded operators. ACM Trans. Math. Softw. 37(1) (2010)

    Google Scholar 

  10. D’Silva, V., Haller, L., Kroening, D.: Abstract conflict driven learning. In: POPL. ACM (2013)

    Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. Giunchiglia, F., Walsh, T.: A theory of abstraction. Artif. Intell. 57(2-3) (1992)

    Google Scholar 

  15. 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

  16. Harrison, J.: Handbook of Practical Logic and Automated Reasoning. Cambridge University Press (2009)

    Google Scholar 

  17. IEEE Comp. Soc.: IEEE Standard for Floating-Point Arithmetic 754-2008 (2008)

    Google Scholar 

  18. 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)

    Chapter  Google Scholar 

  19. Khanh, T.V., Ogawa, M.: SMT for polynomial constraints on real numbers. In: TAPAS. Electronic Notes in Theoretical Computer Science, vol. 289 (2012)

    Google Scholar 

  20. Lapschies, F., Peleska, J., Gorbachuk, E., Mangels, T.: SONOLAR SMT-solver. In: Satisfiability Modulo Theories Competition; System Description (2012)

    Google Scholar 

  21. Melquiond, G.: Floating-point arithmetic in the Coq system. In: Conf. on Real Numbers and Computers. Information & Computation, vol. 216. Elsevier (2012)

    Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. 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)

    Chapter  Google Scholar 

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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

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  • 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

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