Advertisement

Incremental termination proofs and the length of derivations

  • Frank Drewes
  • Clemens Lautemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 488)

Abstract

Incremental termination proofs, a concept similar to termination proofs by quasi-commuting orderings, are investigated. In particular, we show how an incremental termination proof for a term rewriting system T can be used to derive upper bounds on the length of derivations in T. A number of examples show that our results can be applied to yield (sharp) low-degree polynomial complexity bounds.

Keywords

Word Problem Complexity Bound Ground Term Termination Proof Strong Monotonicity 
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. [BD86]
    L. Bachmair, N. Dershowitz: Commutation, transformation, and termination. Proc. 8th Conf. on Automated Deduction, LNCS 230, pp. 5–20.Google Scholar
  2. [BO84]
    G. Bauer, F. Otto: Finite complete rewriting systems and the complexity of the word problem. Acta Informatica 21, pp. 521–540.Google Scholar
  3. [Ch86]
    Ph. le Chenadec: Canonical Forms in Finitely Presented Algebras. J. Wiley & SonsGoogle Scholar
  4. [CL87]
    A. Ben Cherifa, P. Lescanne: Termination of Rewriting Systems by Polynomial Interpretations and its Implementation. Sci. of Comp. Prog. 9, pp. 137–159.Google Scholar
  5. [De82]
    N. Dershowitz: Orderings for Term-rewriting systems. TCS 17, pp. 279–301.Google Scholar
  6. [De87]
    N. Dershowitz: Termination of rewriting. J. Symbolic Computation 3, pp. 69–116.Google Scholar
  7. [DJ89]
    N. Dershowitz, Jean-Pierre Jouannaud: Rewrite systems. Rapport de Recherche no 478, Université de Paris-Sud.Google Scholar
  8. [DL90]
    F. Drewes, C. Lautemann: Incremental Termination Proofs and the Length of Derivations. Universität Bremen, report 7/90.Google Scholar
  9. [EM80]
    H. Ehrig, B. Mahr: Complexity of Implementations on the Level of Algebraic Specifications. Proc. ACM Symp. Theory of Computing.Google Scholar
  10. [HL89]
    D. Hofbauer, C. Lautemann: Termination proofs and the length of derivations. Proc. 3rd Intern. Conf. on Rewriting Techn. and Appl., LNCS 355, pp. 167–177.Google Scholar
  11. [HO80]
    G. Huet, D. Oppen: Equations and rewrite rules: a survey. In Ronald V. Book, Ed.: Formal languages, perspectives and open problems, Academic Press.Google Scholar
  12. [KB70]
    D. E. Knuth, P. B. Bendix: Simple Word Problems in Universal Algebras. In: J. Leech, Ed.: Computational Problems in Abstract Algebra, Oxford, Pergamon Press.Google Scholar
  13. [Kl87]
    J.-W. Klop: Term Rewriting Systems: A Tutorial, EATCS Bulletin 32, pp. 143.Google Scholar
  14. [Ln75]
    D. Lankford: Canonical algebraic simplification in computational logic. Report ATP-25, University of Texas.Google Scholar
  15. [Ln79]
    Dallas Lankford: On proving term rewriting systems are Noetherian. Report MTP-3, Louisiana Tech University.Google Scholar
  16. [St88]
    J. Steinbach: Extension and comparison of simplification orderings. Proc. 3rd Intern. Conf. on Rewriting Techniques and Applications, LNCS 355, pp. 434–448.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Frank Drewes
    • 1
  • Clemens Lautemann
    • 2
  1. 1.Universität BremenGermany
  2. 2.Universität MainzGermany

Personalised recommendations