Locality Results for Certain Extensions of Theories with Bridging Functions

  • Viorica Sofronie-Stokkermans
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)

Abstract

We study possibilities of reasoning about extensions of base theories with functions which satisfy certain recursion (or homomorphism) properties. Our focus is on emphasizing possibilities of hierarchical and modular reasoning in such extensions and combinations thereof. We present practical applications in verification and cryptography.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Armando, A., Ranise, S., Rusinowitch, M.: A rewriting approach to satisfiability procedures. Information and Computation 183(2), 140–164 (2003)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Barrett, C., Shikanian, I., Tinelli, C.: An abstract decision procedure for satisfiability in the theory of inductive data types. Journal on Satisfiability, Boolean Modeling and Computation 3, 1–17 (2007)MathSciNetMATHGoogle Scholar
  3. 3.
    Bonacina, M.P., Echenim, M.: Rewrite-based decision procedures. Electronic Notes in Theoretical Computer Science 174(11), 27–45 (2007)CrossRefMATHGoogle Scholar
  4. 4.
    Comon-Lundh, H., Treinen, R.: Easy intruder deductions. In: Dershowitz, N. (ed.) Verification: Theory and Practice. LNCS, vol. 2772, pp. 225–242. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Comon-Lundh, H.: Challenges in the automated verification of security protocols. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195, pp. 396–409. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Delaune, S.: Easy intruder deduction problems with homomorphisms. Information Processing Letters 97(6), 213–218 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ganzinger, H.: Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems. In: Sixteenth Annual IEEE Symposium on Logic in Computer Science, Boston, MA, USA, pp. 81–90. IEEE Computer Society, Los Alamitos (2001)Google Scholar
  8. 8.
    Ganzinger, H., Sofronie-Stokkermans, V., Waldmann, U.: Modular proof systems for partial functions with Evans equality. Information and Computation 204(10), 1453–1492 (2006)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Givan, R., McAllester, D.: New results on local inference relations. In: Principles of Knowledge Representation and reasoning: Proceedings of the Third International Conference (KR 1992), pp. 403–412. Morgan Kaufmann Press, San Francisco (1992)Google Scholar
  10. 10.
    Givan, R., McAllester, D.A.: Polynomial-time computation via local inference relations. ACM Transactions on Computational Logic 3(4), 521–541 (2002)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On local reasoning in verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Ihlemann, C., Sofronie-Stokkermans, V.: System description. H-PiLOT. In: Schmidt, R.A. (ed.) CADE 2009. LNCS (LNAI), vol. 5663, pp. 131–139. Springer, Heidelberg (2009)Google Scholar
  13. 13.
    Oppen, D.C.: Reasoning about recursively defined data structures. Journal of the ACM 27(3), 403–411 (1980)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Sofronie-Stokkermans, V.: Hierarchic reasoning in local theory extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 219–234. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Sofronie-Stokkermans, V.: Hierarchical and modular reasoning in complex theories: The case of local theory extensions. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS, vol. 4720, pp. 47–71. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Sofronie-Stokkermans, V., Ihlemann, C.: Automated reasoning in some local extensions of ordered structures. Journal of Multiple-Valued Logics and Soft Computing 13(4-6), 397–414 (2007)MathSciNetMATHGoogle Scholar
  17. 17.
    Sofronie-Stokkermans, V.: Efficient hierarchical reasoning about functions over numerical domains. In: Dengel, A.R., Berns, K., Breuel, T.M., Bomarius, F., Roth-Berghofer, T.R. (eds.) KI 2008. LNCS (LNAI), vol. 5243, pp. 135–143. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Zhang, T., Sipma, H., Manna, Z.: Decision procedures for term algebras with integer constraints. Information and Computation 204(10), 1526–1574 (2006)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Viorica Sofronie-Stokkermans
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations