Abstract
This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalized membership problem (extending the emptiness problem) is decidable by proving that the saturation of tree automata presentations with suitable paramodulation strategies terminates. Alternatively our results can be viewed as new decidable classes of first-order formula.
This work has been partially supported by the research projects RNTL PROUVÉ (No 03 V 360) and ACI–SI SATIN and ROSSIGNOL.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: 28th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 104–115 (2001)
Bachmair, L., Ganzinger, H., Lynch, C., Snyder, W.: Basic Paramodulation. Information and Computation 121(2), 172–192 (1995)
Bogaert, B., Tison, S.: Equality and Disequality Constraints on Direct Subterms in Tree Automata. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 161–171. Springer, Heidelberg (1992)
Bull, J.A., Otway, D.J.: The authentication protocol. Technical report, Defence Research Agency, Malvern, UK (1997)
Caron, A.-C., Comon, H., Coquidé, J.-L., Dauchet, M., Jacquemard, F.: Pumping, Cleaning and Symbolic Constraints Solving. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 436–449. Springer, Heidelberg (1994)
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (1997), http://www.grappa.univ-lille3.fr/tata
Dauchet, M., Caron, A.-C., Coquidé, J.-L.: Automata for Reduction Properties Solving. Journal of Symbolic Computation 20(2), 215–233 (1995)
Denning, D.E., Sacco, G.M.: Timestamps in Key Distribution Protocols. In: Communications of the ACM (1981)
Dershowitz, N., Jouannaud, J.-P.: Handbook of Theoretical Computer Science. In: Rewrite systems, vol. B, pp. 243–320. Elsevier, Amsterdam (1990)
Devienne, P., Talbot, J.-M., Tison, S.: Set-based analysis for logic programming and tree automata. In: Van Hentenryck, P. (ed.) SAS 1997. LNCS, vol. 1302, pp. 127–140. Springer, Heidelberg (1997)
Frühwirth, T., Shapiro, E., Vardi, M., Yardeni, E.: Logic programs as types for logic programs. In: Proc. of the 6th IEEE Symposium on Logic in Computer Science, pp. 300–309 (1991)
Genet, T., Klay, F.: Rewriting for Cryptographic Protocol Verification. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, Springer, Heidelberg (2000)
Goubault-Larrecq, J.: Deciding \(\mathcal{\MakeUppercase{H}}_1\) by Resolution. Information Processing Letters 95(3), 401–408 (2005)
Jacquemard, F., Meyer, C., Weidenbach, C.: Unification in Extensions of Shallow Equational Theories. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 76–90. Springer, Heidelberg (1998)
Jacquemard, F., Rusinowitch, M., Vigneron, L.: Tree automata with equality constraints modulo equational theories. Technical Report LSV-06-07, LSV (2006), http://www.lsv.ens-cachan.fr/Publis
Küsters, R., Wilke, T.: Automata-Based Analysis of Recursive Cryptographic Protocols. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 382–393. Springer, Heidelberg (2004)
Lynch, C., Meadows, C.: On the relative soundness of the free algebra model for public key encryption. Electr. Notes Theor. Comput. Sci. 125(1), 43–54 (2005)
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)
Nieuwenhuis, R., Rubio, A.: Handbook of Automated Reasoning, ch. 7. In: Nieuwenhuis, R., Rubio, A. (eds.) Paramodulation-Based Theorem Proving, vol. I, Elsevier Science and MIT Press (2001)
Ohsaki, H., Takai, T.: Decidability and Closure Properties of Equational Tree Languages. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 114–128. Springer, Heidelberg (2002)
Riazanov, A., Voronkov, A.: Splitting Without Backtracking. In: Proc. of the 17th Int. Joint Conf. on Artificial Intelligence, IJCAI, pp. 611–617. Morgan Kaufmann, San Francisco (2001)
Seki, H., Takai, T., Fujinaka, Y., Kaji, Y.: Layered Transducing Term Rewriting System and Its Recognizability Preserving Property. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 98–113. Springer, Heidelberg (2002)
Tison, S.: Tree automata and term rewrite systems. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, Springer, Heidelberg (2000)
Truderung, T.: Selecting theories and recursive protocols. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 217–232. Springer, Heidelberg (2005)
Verma, K.N.: Two-Way Equational Tree Automata. PhD thesis, ENS Cachan (September 2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jacquemard, F., Rusinowitch, M., Vigneron, L. (2006). Tree Automata with Equality Constraints Modulo Equational Theories. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_45
Download citation
DOI: https://doi.org/10.1007/11814771_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37187-8
Online ISBN: 978-3-540-37188-5
eBook Packages: Computer ScienceComputer Science (R0)