Aligators for Arrays (Tool Paper)

  • Thomas A. Henzinger
  • Thibaud Hottelier
  • Laura Kovács
  • Andrey Rybalchenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


This paper presents Aligators, a tool for the generation of universally quantified array invariants. Aligators leverages recurrence solving and algebraic techniques to carry out inductive reasoning over array content. The Aligators’ loop extraction module allows treatment of multi-path loops by exploiting their commutativity and serializability properties. Our experience in applying Aligators on a collection of loops from open source software projects indicates the applicability of recurrence and algebraic solving techniques for reasoning about arrays.


Loop Counter Invariant Generation Array Variable Loop Body Algebraic Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Buchberger, B.: An Algorithm for Finding the Basis Elements of the Residue Class Ring of a Zero Dimensional Polynomial Ideal. J. of Symbolic Computation 41(3-4), 475–511 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs (1976)zbMATHGoogle Scholar
  4. 4.
    Smith, M., et al.: The OggEnc Home Page (1994),
  5. 5.
    Leroy, X., et al.: The Objective Caml system - release 3.11. INRIA (2008)Google Scholar
  6. 6.
    Gailly, J., Adler, M.: The Gzip Home Page (1991),
  7. 7.
    Gopan, D., Reps, T.W., Sagiv, S.: A Framework for Numeric Analysis of Array Operations. In: Proc. of POPL, pp. 338–350 (2005)Google Scholar
  8. 8.
    Gulwani, S., Jain, S., Koskinen, E.: Control-flow Refinement and Progress Invariants for Bound Analysis. In: Proc. of PLDI, pp. 375–385 (2009)Google Scholar
  9. 9.
    Gulwani, S., Tiwari, A.: Combining Abstract Interpreters. In: Proc. of PLDI, pp. 376–386 (2006)Google Scholar
  10. 10.
    Gupta, A., Rybalchenko, A.: InvGen: An Efficient Invariant Generator. In: Bouajjani, A., Maler, O. (eds.) Computer Aided Verification. LNCS, vol. 5643, pp. 634–640. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Halbwachs, N., Péron, M.: Discovering Properties about Arrays in Simple Programs. In: Proc. of PLDI, pp. 339–348 (2008)Google Scholar
  12. 12.
    Henzinger, T.A., Hottelier, T., Kovács, L.: Valigator: A Verification Tool with Bound and Invariant Generation. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 333–342. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Henzinger, T.A., Hottelier, T., Kovács, L., Voronkov, A.: Invariant and Type Inference for Matrices. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 163–179. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Jhala, R., McMillan, K.L.: Array Abstractions from Proofs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 193–206. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Kovács, L.: Reasoning Algebraically About P-Solvable Loops. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 249–264. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Kovács, L., Voronkov, A.: Finding Loop Invariants for Programs over Arrays Using a Theorem Prover. In: Chechik, M., Wirsing, M. (eds.) FASE 2009. LNCS, vol. 5503, pp. 470–485. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Seward, J.: The Bzip2 Home Page (1996),
  18. 18.
    Srivastava, S., Gulwani, S.: Program Verification using Templates over Predicate Abstraction. In: Proc. of PLDI, pp. 223–234 (2009)Google Scholar
  19. 19.
    Wolfram, S.: The Mathematica Book. Version 5.0. Wolfram Media (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Thomas A. Henzinger
    • 1
  • Thibaud Hottelier
    • 2
  • Laura Kovács
    • 3
  • Andrey Rybalchenko
    • 4
  1. 1.ISTAustria
  2. 2.UC BerkeleyUSA
  3. 3.TU ViennaAustria
  4. 4.TUMGermany

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