A New Acceleration-Based Combination Framework for Array Properties

  • Francesco Alberti
  • Silvio Ghilardi
  • Natasha Sharygina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9322)


This paper presents an acceleration-based combination framework for checking the satisfiability of classes of quantified formulae of the theory of arrays. We identify sufficient conditions for which an ‘acceleratability’ result can be used as a black-box module inside such satisfiability procedures. Besides establishing new decidability results and relating them to results from recent literature, we discuss the application of our combination framework to the problem of checking the safety of imperative programs with arrays.


Equivalence Class Proof Obligation Array Variable Reachability Problem Acceleration Module 
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  1. 1.
    Aho, A.V., Lam, M.S., Sethi, R., Ullman, J.: Compilers: Principles, Techniques, and Tools. Addison-Wesley Educational Publishers, Incorporated (2007)Google Scholar
  2. 2.
    Alberti, F., Ghilardi, S., Sharygina, N.: Definability of accelerated relations in a theory of arrays and its applications. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS, vol. 8152, pp. 23–39. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Alberti, F., Ghilardi, S., Sharygina, N.: Booster: an acceleration-based verification framework for array programs. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 18–23. Springer, Heidelberg (2014)Google Scholar
  4. 4.
    Alberti, F., Ghilardi, S., Sharygina, N.: Decision procedures for flat array properties. In: TACAS, pp. 15–30 (2014)Google Scholar
  5. 5.
    Alberti, F., Ghilardi, S., Sharygina, N.: A new acceleration-based combination framework for array properties, Avalilable from authors’ webpages (2015)Google Scholar
  6. 6.
    Boigelot, B.: On iterating linear transformations over recognizable sets of integers. Theor. Comput. Sci. 309(1), 413–468 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bozga, M., Gîrlea, C., Iosif, R.: Iterating octagons. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 337–351. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Bozga, M., Iosif, R., Konečný, F.: Fast acceleration of ultimately periodic relations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 227–242. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Bozga, M., Iosif, R., Lakhnech, Y.: Flat parametric counter automata. Fundamenta Informaticae (91), 275–303 (2009)Google Scholar
  10. 10.
    Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Comon, H., Jurski, Y.: Multiple counters automata, safety analysis and presburger arithmetic. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 268–279. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Finkel, A., Leroux, J.: How to compose Presburger-accelerations: Applications to broadcast protocols. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 145–156. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Gurfinkel, A., Chaki, S., Sapra, S.: Efficient predicate abstraction of program summaries. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 131–145. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Habermehl, P., Iosif, R., Vojnar, T.: A logic of singly indexed arrays. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 558–573. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Halpern, J.Y.: Presburger arithmetic with unary predicates is \(\Pi^1_1\) complete. J. Symbolic Logic 56(2), 637–642 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Semënov, A.L.: Logical theories of one-place functions on the set of natural numbers. Izvestiya: Mathematics 22, 587–618 (1984)CrossRefzbMATHGoogle Scholar
  18. 18.
    Shoenfield, J.R.: Mathematical logic. Association for Symbolic Logic, Urbana, IL, 2001. Reprint of the 1973 second printingGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Francesco Alberti
    • 1
  • Silvio Ghilardi
    • 2
  • Natasha Sharygina
    • 3
  1. 1.Fondazione Centro San RaffaeleMilanItaly
  2. 2.Università degli Studi di MilanoMilanItaly
  3. 3.Università della Svizzera ItalianaLuganoSwitzerland

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