A Sufficient Completeness Checker for Linear Order-Sorted Specifications Modulo Axioms

  • Joe Hendrix
  • José Meseguer
  • Hitoshi Ohsaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)


We present a tool for checking the sufficient completeness of left-linear, order-sorted equational specifications modulo associativity, commutativity, and identity. Our tool treats this problem as an equational tree automata decision problem using the tree automata library CETA, which we also introduce in this paper. CETA implements a semi-algorithm for checking the emptiness of a class of tree automata that are closed under Boolean operations and an equational theory containing associativity, commutativity and identity axioms. Though sufficient completeness for this class of specifications is undecidable in general, our tool is a decision procedure for subcases known to be decidable, and has specialized techniques that are effective in practice for the general case.


Tree Automaton Inductive Theorem Emptiness Problem Constructor Term Regular Tree Language 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bouhoula, A., Jacquemard, F.: Automatic verification of sufficient completeness for conditional constrained term rewriting systems. Technical Report LSC-05-17, ENS de Cachan (2006), available at http://www.lsv.ens-cachan.fr/Publis/
  2. 2.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications, (1997) (release October 1, 2002), available at: http://www.grappa.univ-lille3.fr/tata
  3. 3.
    Comon, H., Jacquemard, F.: Ground reducibility is EXPTIME-complete. Information and Computation 187(1), 123–153 (2003)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Guttag, J.V., Horning, J.J.: The algebraic specification of abstract data types. Acta Informatica 10, 27–52 (1978)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hendrix, J., Clavel, M., Meseguer, J.: A sufficient completeness reasoning tool for partial specifications. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 165–174. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Hendrix, J., Ohsaki, H., Meseguer, J.: Sufficient completeness checking with propositional tree automata. Technical Report UIUCDCS-R-2005-2635, University of Illinois at Urbana-Champaign (2005), available at: http://maude.cs.uiuc.edu/tools/scc/
  7. 7.
    Hendrix, J., Ohsaki, H., Viswanathan, M.: Propositional Tree Automata. Technical Report UIUCDCS-R-2006-2695, University of Illinois at Urbana-Champaign (2006), available at: http://maude.cs.uiuc.edu/tools/scc/
  8. 8.
    Kapur, D., Narendran, P., Rosenkrantz, D.J., Zhang, H.: Sufficient-completeness, ground-reducibility and their complexity. Acta Informatica 28(4), 311–350 (1991)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kapur, D., Narendran, P., Zhang, H.: On sufficient-completeness and related properties of term rewriting systems. Acta Informatica 24(4), 395–415 (1987)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ohsaki, H.: Beyond Regularity: Equational Tree Automata for Associative and Commutative Theories. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 539–553. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Ohsaki, H., Takai, T.: ACTAS: A system design for associative and commutative tree automata theory. In: Proc. of RULE. ENTCS, vol. 124, pp. 97–111. Elsevier, Amsterdam (2005)Google Scholar
  13. 13.
    Viry, P.: Equational rules for rewriting logic. Theoretical Computer Science 285(2), 487–517 (2002)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joe Hendrix
    • 1
  • José Meseguer
    • 1
  • Hitoshi Ohsaki
    • 2
  1. 1.University of Illinois at Urbana-Champaign 
  2. 2.National Institute of Advanced Industrial Science and Technology 

Personalised recommendations