Skip to main content
SpringerLink
Log in

Negation Elimination from Simple Equational Formulae

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1853))

Included in the following conference series:

Abstract

Equational formulae are first-order formulae over an alphabet F of function symbols whose only predicate symbol is syntactic equality. Unification problems are an important special case of equational formulae, where no universal quantifiers and no negation occur. By the negation elimination problem we mean the problem of deciding whether a given equational formula is semantically equivalent to a unification problem. This decision problem has many interesting applications in machine learning, logic programming, functional programming, constrained rewriting, etc. In this work we present a new algorithm for the negation elimination problem of equational formulae with purely existential quantifier prefix. Moreover, we prove the coNP-completeness for equational formulae in DNF and the D 2 p-hardness in case of CNF.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Comon, C. Delor: Equational Formulae with Membership Constraints, Journal of Information and Computation, Vol 112, pp. 167–216 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  2. H. Comon, P. Lescanne: Equational Problems and Disunification, Journal of Symbolic Computation, Vol 7, pp. 371–425 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Fernández: Negation Elimination in Empty or Permutative Theories, Journal of Symbolic Computation, Vol 26, pp. 97–133 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Gottlob, R. Pichler: Working with ARMs: Complexity Results on Atomic Representations of Herbrand Models, in Proceedings of LICS’99, pp. 306–315, IEEE Computer Society Press, (1999).

    Google Scholar 

  5. C. Kirchner, H. Kirchner, M. Rusinowitch: Deduction with symbolic constraints, Revue Française d’Intelligence Artificielle, Vol 4, pp. 9–52 (1990).

    Google Scholar 

  6. G. Kuper, K. McAloon, K. Palem, K. Perry: Efficient Parallel Algorithms for Anti-Unification and Relative Complement, in Proceedings of LICS’88, pp. 112–120, IEEE Computer Society Press (1988).

    Google Scholar 

  7. K. Kunen: Answer Sets and Negation as Failure, in Proceedings of the Fourth Int. Conf. on Logic Programming, Melbourne, pp. 219–228 (1987).

    Google Scholar 

  8. J.-L. Lassez, K. Marriott: Explicit Representation of Terms defined by Counter Examples, Journal of Automated Reasoning, Vol 3, pp. 301–317 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  9. J.-L. Lassez, M. Maher, K. Marriott: Elimination of Negation in Term Algebras, in Proceedings of MFCS’91, LNCS 520, pp. 1–16, Springer (1991).

    Google Scholar 

  10. M. Maher, P. Stuckey: On Inductive Inference of Cyclic Structures, Annals of Mathematics and Artificial Intelligence Vol 15 No 2, pp. 167–208, (1995).

    Article  MATH  MathSciNet  Google Scholar 

  11. K. Marriott: Finding Explicit Representations for Subsets of the Herbrand Universe, PhD Thesis, The University of Melbourne, Australia (1988).

    Google Scholar 

  12. A. Martelli, U. Montanari: An efficient unification algorithm, ACM Transactions on Programming Languages and Systems, Vol 4 No 2, pp. 258–282 (1982).

    Article  MATH  Google Scholar 

  13. R. Pichler: The Explicit Representability of Implicit Generalizations, to appear in Proceedings of RTA’2000, Springer (2000).

    Google Scholar 

  14. R. Pichler: Negation Elimination from Simple Equational Formulae, full paper, available from the author (2000).

    Google Scholar 

  15. L. J. Stockmeyer: The Polynomial Time Hierarchy, in Journal of Theoretical Computer Science, Vol 3, pp. 1–12 (1976).

    Article  MathSciNet  Google Scholar 

  16. M. Tajine: The negation elimination from syntactic equational formulas is decidable, in Proceedings of RTA’93, pp. 316–327, LNCS 690, Springer (1993).

    Google Scholar 

  17. S. Vorobyov: An Improved Lower Bound for the Elementary Theories of Trees, in Proceedings of CADE-13, LNAI 1104, pp. 275–287, Springer (1996).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Wien, Germany

    Reinhard Pichler

Authors
  1. Reinhard Pichler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Ugo Montanari

  2. Center for Computer Sciences, University of Geneva, 24, Rue Général Dufour, 1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. Department of Computer Sciences, ETH Zurich, 8092, Zurich, Switzerland

    Emo Welzl

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pichler, R. (2000). Negation Elimination from Simple Equational Formulae. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_52

Download citation

  • DOI: https://doi.org/10.1007/3-540-45022-X_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67715-4

  • Online ISBN: 978-3-540-45022-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation