Crossing the Syntactic Barrier: Hom-Disequalities for \({\mathcal H}_1\)-Clauses

  • Andreas Reuß
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)

Abstract

We extend \({\mathcal H}_1\)-clauses with disequalities between images of terms under a tree homomorphism (hom-disequalities). This extension allows to test whether two terms are distinct modulo a semantic interpretation, allowing, e.g., to neglect information that is not considered relevant for the intended comparison. We prove that \({\mathcal H}_1\)-clauses with hom-disequalities are more expressive than \({\mathcal H}_1\)-clauses with ordinary term disequalities, and that they are incomparable with \({\mathcal H}_1\)-clauses with disequalities between paths. Our main result is that \({\mathcal H}_1\)-clauses with this new type of constraints can be normalized into an equivalent tree automaton with hom-disequalities. Since emptiness for that class of automata turns out to be decidable, we conclude that satisfiability is decidable for positive Boolean combinations of queries to predicates defined by \({\mathcal H}_1\)-clauses with hom-disequalities.

Keywords

Horn Clause Cryptographic Protocol Ground Term Tree Automaton Unary Predicate 
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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References

  1. 1.
    Blanchet, B.: An efficient cryptographic protocol verifier based on prolog rules. In: CSFW, pp. 82–96 (2001)Google Scholar
  2. 2.
    Bugliesi, M., Rossi, S.: Non-interference proof techniques for the analysis of cryptographic protocols. Journal of Computer Security 13(1), 87–113 (2005)Google Scholar
  3. 3.
    Chatzikokolakis, K.: Probabilistic and Information-Theoretic Approaches to Anonymity. Ph.D. thesis, École polytechnique (2007)Google Scholar
  4. 4.
    Frühwirth, T.W., Shapiro, E.Y., Vardi, M.Y., Yardeni, E.: Logic programs as types for logic programs. In: LICS, pp. 314–328 (1991)Google Scholar
  5. 5.
    Godoy, G., Giménez, O., Ramos, L., Àlvarez, C.: The hom problem is decidable. In: STOC, pp. 485–494. ACM (2010)Google Scholar
  6. 6.
    Goguen, J.A., Meseguer, J.: Security policies and security models. In: IEEE Symposium on Security and Privacy, pp. 11–20 (1982)Google Scholar
  7. 7.
    Goubault-Larrecq, J.: Deciding H1 by resolution. IPL 95(3), 401–408 (2005)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Goubault-Larrecq, J., Parrennes, F.: Cryptographic Protocol Analysis on Real C Code. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 363–379. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Nielson, F., Riis Nielson, H., Seidl, H.: Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 20–35. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Reuß, A., Seidl, H.: Bottom-Up Tree Automata with Term Constraints. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 581–593. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Seidl, H., Neumann, A.: On Guarding Nested Fixpoints. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 484–498. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Seidl, H., Reuß, A.: Extending H1-clauses with disequalities. IPL 111(20), 1007–1013 (2011)CrossRefGoogle Scholar
  13. 13.
    Seidl, H., Reuß, A.: Extending \({\cal H}_1\)-Clauses with Path Disequalities. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 165–179. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Weidenbach, C.: Towards an Automatic Analysis of Security Protocols in First-Order Logic. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 314–328. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas Reuß
    • 1
  • Helmut Seidl
    • 1
  1. 1.Technische Universität MünchenGermany

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