Advertisement

On the word, subsumption, and complement problem for recurrent term schematizations

Extended abstract
  • Miki Hermann
  • Gernot Salzer
Contributed Papers Rewriting
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)

Abstract

We investigate the word and the subsumption problem for recurrent term schematizations, which are a special type of constraints based on iteration. By means of unification, we reduce these problems to a fragment of Presburger arithmetic. Our approach is applicable to all recurrent term schematizations having a finitary unification algorithm. Furthermore, we study a particular form of the complement problem. Given a finite set of terms, we ask whether its complement can be finitely represented by schematizations, using only the equality predicate without negation. The answer is negative as there are ground terms too complex to be represented by schematizations with limited resources.

Keywords

Word Problem Unification Algorithm Counter Variable Quantifier Elimination Complement Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AHL97]
    A. Amaniss, M. Hermann, and D. Lugiez. Set operations for recurrent term schematizations. In M. Bidoit and M. Dauchet, editors, Proc. 7th TAPSOFT Conference, Lille (France), LNCS 1214, pages 333–344. Springer, 1997.Google Scholar
  2. [CH95]
    H. Chen and J. Hsiang. Recurrence domains: Their unification and application to logic programming. Information and Computation, 122:45–69, 1995.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [Com95]
    H. Comon. On unification of terms with integer exponents. Mathematical Systems Theory, 28(1):67–88, 1995.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [Coo72]
    D.C. Cooper. Theorem proving in arithmetic without multiplication. In B. Meltzer and D. Mitchie, editors, Machine Intelligence, volume 7, pages 91–99. Edinburgh University Press, 1972.Google Scholar
  5. [GJ79]
    M.R. Garey and D.S. Johnson. Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman and Co, 1979.Google Scholar
  6. [Grä88]
    E. Grädel. Subclasses of Preburger arithmetic and the polynomial-time hierarchy. Theoretical Computer Science, 56(3):289–301, 1988.zbMATHMathSciNetCrossRefGoogle Scholar
  7. [HG97]
    M. Hermann and R. Galbavý. Unification of infinite sets of terms schematized by primal grammars. Theoretical Computer Science, 176(1–2):111–158, 1997.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [LM87]
    J.-L. Lassez and K. Marriott. Explicit representation of terms defined by counter examples. J. Automated Reasoning, 3(3):301–317, 1987.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [Pel97]
    N. Peltier. Increasing model building capabilities by constraint solving on terms with integer exponents. J. Symbolic Computation, 24(1):59–101, 1997.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [Sal91]
    G. Salzer. Deductive generalization and meta-reasoning, or how to formalize Genesis. In österreichische Tagung für Künstliche Intelligenz, Informatik-Fachberichte 287, pages 103–115. Springer, 1991.Google Scholar
  11. [Sal92]
    G. Salzer. The unification of infinite sets of terms and its applications. In A. Voronkov, editor, Proc. 3rd LPAR Conference, St. Petersburg (Russia), LNCS (LNAI) 624, pages 409–420. Springer, 1992.Google Scholar
  12. [Sal94]
    G. Salzer. Primal grammars and unification modulo a binary clause. In A. Bundy, editor, Proc. 12th CADE Conference, Nancy (France), LNCS (LNAI) 814, pages 282–295. Springer, 1994.Google Scholar
  13. [Sch97]
    U. Schöning. Complexity of Presburger arithmetic with fixed quantifier dimension. Theory of Computing Systems, 30(4):423–428, 1997.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Miki Hermann
    • 1
  • Gernot Salzer
    • 2
  1. 1.LORIA (CNRS)Vandœuvre-lès-NancyFrance
  2. 2.Technische Universität WienWienAustria

Personalised recommendations