International Symposium on Frontiers of Combining Systems

Frontiers of Combining Systems pp 119-134 | Cite as

Weakly Equivalent Arrays

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9322)

Abstract

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. In this paper, we present an efficient decision procedure for the theory of arrays. We build upon the notion of weak equivalence. Intuitively, two arrays are weakly equivalent if they only differ at finitely many indices. We formalise this notion and show how to exploit weak equivalences to decide formulas in the quantifier-free fragment of the theory of arrays. We present a novel data structure to represent all weak equivalence classes induced by a formula in linear space (in the number of array terms). Experimental evidence shows that this technique is competitive with other approaches.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures. ACM Trans. Comput. Log. 10(1) (2009)Google Scholar
  2. 2.
    Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB Standard: 2.0. In: SMT (2010)Google Scholar
  3. 3.
    Brummayer, R., Biere, A.: Lemmas on demand for the extensional theory of arrays. JSAT 6(1-3), 165–201 (2009)MathSciNetMATHGoogle Scholar
  4. 4.
    Bruttomesso, R., Ghilardi, S., Ranise, S.: Quantifier-free interpolation of a theory of arrays. Logical Methods in Computer Science 8(2) (2012)Google Scholar
  5. 5.
    Christ, J., Hoenicke, J.: Weakly equivalent arrays. CoRR mabs/1405.6939 (2014). http://arxiv.org/abs/1405.6939
  6. 6.
    Christ, J., Hoenicke, J., Nutz, A.: SMTInterpol: An interpolating SMT solver. In: Donaldson, A., Parker, D. (eds.) SPIN 2012. LNCS, vol. 7385, pp. 248–254. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Christ, J., Hoenicke, J., Nutz, A.: Proof tree preserving interpolation. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 124–138. Springer, Heidelberg (2013)Google Scholar
  8. 8.
    Craig, W.: Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. J. Symb. Log. 22(3), 269–285 (1957)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast decision procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    McCarthy, J.: Towards a mathematical science of computation. In: IFIP Congress, pp. 21–28 (1962)Google Scholar
  11. 11.
    de Moura, L., Bjørner, N.: Generalized, efficient array decision procedures. In: FMCAD, pp. 45–52 (2009)Google Scholar
  12. 12.
    Nieuwenhuis, R., Oliveras, A.: Proof-producing congruence closure. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 453–468. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Ranise, S., Ringeissen, C., Zarba, C.G.: Combining data structures with nonstably infinite theories using many-sorted logic. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 48–64. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Stump, A., Barrett, C.W., Dill, D.L., Levitt, J.R.: A decision procedure for an extensional theory of arrays. In: LICS, pp. 29–37. IEEE Computer Society (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of FreiburgFreiburgGermany

Personalised recommendations