LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals

(Tool Paper)
  • Bernd Becker
  • Christian Dax
  • Jochen Eisinger
  • Felix Klaedtke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4590)

Abstract

The mechanization of many verification tasks relies on efficient implementations of decision procedures for fragments of first-order logic. Interactive theorem provers like pvs also make use of such decision procedures to increase the level of automation. Our tool lira implements decision procedures based on automata-theoretic techniques for first-order logics with linear arithmetic, namely, for FO(ℕ, +), FO(ℤ,+,<), and FO(ℝ, ℤ,+,<).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bardin, S., Leroux, J., Point, G.: FAST extended release. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 63–66. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Boigelot, B., Jodogne, S., Wolper, P.: An effective decision procedure for linear arithmetic over the integers and reals. ACM Trans. Comput. Log 6, 614–633 (2005)CrossRefGoogle Scholar
  3. 3.
    Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T.A., van Rossum, P., Schulz, S., Sebastiani, R.: The MathSAT 3 system. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 3632, pp. 315–321. Springer, Heidelberg (2001)Google Scholar
  4. 4.
    Büchi, J.: Weak second-order arithmetic and finite automata. Zeitschrift der mathematischen Logik und Grundlagen der Mathematik 6, 66–92 (1960)MATHCrossRefGoogle Scholar
  5. 5.
    Couvreur, J.-M.: A BDD-like implementation of an automata package. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 310–311. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    CUDD, Colorado university Decision Diagram package. http://vlsi.colorado.edu/~fabio/CUDD/
  7. 7.
    Damm, W., Disch, S., Hungar, H., Pang, J., Pigorsch, F., Scholl, C., Waldmann, U., Wirtz, B.: Automatic verification of hybrid systems with large discrete state space. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 276–291. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Dax, C., Eisinger, J., Klaedtke, F.: Mechanizing the powerset construction for restricted classes of ω-automata, Tech. Rep. 228, Institut für Informatik, Albert-Ludwigs-Universität Freiburg (2007)Google Scholar
  9. 9.
    Dutertre, B., de Moura, L.: The Yices SMT solver (2006), available at http://yices.csl.sri.com/tool-paper.pdf
  10. 10.
    Eisinger, J., Klaedtke, F.: Don’t care words with an application to the automata-based approach for real addition. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 67–80. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Klarlund, N.: A theory of restrictions for logics and automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 406–417. Springer, Heidelberg (1999)Google Scholar
  12. 12.
    Klarlund, N., Møller, A., Schwartzbach, M.I.: MONA implementation secrets. Int. J. Found. Comput. Sci. 13, 571–586 (2002)MATHCrossRefGoogle Scholar
  13. 13.
    lash, The Liège Automata-based Symbolic Handler, http://www.montefiore.ulg.ac.be/~boigelot/research/lash/
  14. 14.
    omega, The Omega project, http://www.cs.umd.edu/projects/omega/

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Bernd Becker
    • 1
  • Christian Dax
    • 2
  • Jochen Eisinger
    • 1
  • Felix Klaedtke
    • 2
  1. 1.Albert-Ludwigs-Universität FreiburgGermany
  2. 2.ETH ZurichSwitzerland

Personalised recommendations