Ground reducibility and automata with disequality constraints

  • Hubert Comon
  • Florent Jacquemard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)


Using the automata with constraints, we give an algorithm for the decision of ground reducibility of a term t w.r.t. a rewriting system R. The complexity of the algorithm is doubly exponential in the maximum of the depths of t and R and the cardinal of R.


Equality Constraint Close Equality Ground Term Tree Automaton Ground Instance 
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  1. [1]
    B. Bogaert and S. Tison. Equality and disequality constraints on brother terms in tree automata. In A. Finkel, editor, Proc. 9th Symp. on Theoretical Aspects of Computer Science, Paris, 1992. Springer-Verlag.Google Scholar
  2. [2]
    R. Bündgen and W. Küchlin. Computing ground reductibility and inductively complete positions. Universitaet Tübingen, Oct. 1988.Google Scholar
  3. [3]
    A.-C. Caron, J.-L. Coquidé, and M. Dauchet. Encompassment properties and automata with constraints. In Proc. RTA 93, 1993.Google Scholar
  4. [4]
    H. Comon. Unification et disunification: Théorie et applications. Thèse de Doctorat, Institut National Polytechnique de Grenoble, France, 1988.Google Scholar
  5. [5]
    N. Dershowitz and J.-P. Jouannaud. Notations for rewriting. EATCS Bulletin, 43:162–172, 1990.Google Scholar
  6. [6]
    M. Gécseg and M. Steinby. Tree Automata. Akademia Kiadó, Budapest, 1984.Google Scholar
  7. [7]
    J.-P. Jouannaud and E. Kounalis. Automatic proofs by induction in theories without constructors. Information and Computation, 82(1), July 1989.Google Scholar
  8. [8]
    D. Kapur, P. Narendran, D. Rosenkrantz, and H. Zhang. Sufficient completeness, ground reducibility and their complexity. Acta Inf., 28:311–350, 1991.Google Scholar
  9. [9]
    D. Kapur, P. Narendran, and H. Zhang. On sufficient completeness and related properties of term rewriting systems. Acta Inf., 24(4):395–415, 1987.Google Scholar
  10. [10]
    E. Kounalis. Completeness in data type specifications. In Proc. EUROCAL 85, Linz, LNCS 204, Pages 348–362. Springer-Verlag, Apr. 1985.Google Scholar
  11. [11]
    E. Kounalis. Testing for the ground (co)-reducibility in term rewriting systems. Theoretical Comput. Sci., 106(1):87–117, 1992.Google Scholar
  12. [12]
    T. Nipkow and G. Weikum. A decidability result about sufficient completeness of axiomatically specified abstract data types. In Proc. 6th GI Conf. Springer-Verlag, 1982.Google Scholar
  13. [13]
    D. Plaisted. Semantic confluence tests and completion methods. Information and Control, 65:182–215, 1985.Google Scholar
  14. [14]
    M. Rabin. Decidable theories. In J. Barwise, editor, Handbook of Mathematical Logic, pages 595–629. North-Holland, 1977.Google Scholar
  15. [15]
    W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 134–191. Elsevier, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Hubert Comon
    • 1
  • Florent Jacquemard
    • 1
  1. 1.Laboratoire de Recherche en Informatique. CNRS URA 410Univ. Paris-SudOrsay cedexFrance

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