Skip to main content

A Fully Syntactic AC-RPO

  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1631))

Included in the following conference series:

Abstract

We present the first fully syntactic (i.e., non-interpretationbased) AC-compatible recursive path ordering (RPO). It is simple, and hence easy to implement, and its behaviour is intuitive as in the standard RPO. The ordering is AC-total, and defined uniformly for both ground and non-ground terms, as well as for partial precedences. More importantly, it is the first one that can deal incrementally with partial precedences, an aspect that is essential, together with its intuitive behaviour, for interactive applications like Knuth-Bendix completion.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. L. Bachmair. Associative-commutative reduction orderings. Information Processing Letters, 43:21–27, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Ben-Cherifa and P. Lescanne. Termination of rewriting systems by polynomial interpretations and its implementation. Science of Computer Programming, 9:137–160, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. Bachmair and D. A. Plaisted. Termination orderings for associativecommutative rewriting systems. J. of Symbolic Comput., 1:329–349, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Comon, R. Nieuwenhuis, and A. Rubio. Orderings, AC-Theories and Symbolic Constraint Solving. In 10th Annual IEEE Symp. on Logic in Computer Science, pp. 375–385, San Diego, 1995. IEEE Comput. Society Press.

    Google Scholar 

  5. N. Dershowitz. Orderings for term-rewriting systems. Theoretical Computer Science, 17(3):279–301, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  6. N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associativecommutative rewriting. In Int. Joint Conf. on Artificial Inteligence, pp. 940–944, 1983.

    Google Scholar 

  7. C. Delor and L. Puel. Extension of the associative path ordering to a chain of associative commutative symbols. In 5th Int. Conf. on Rewriting Techniques and Applications, LNCS 690, pp. 389–404, Montreal, 1993. Springer-Verlag.

    Google Scholar 

  8. I. Gnaedig and P. Lescanne. Proving termination of associative-commutative rewrite systems by rewriting. In 8th International Conference on Automated Deduction, LNCS 230, pp. 52–61, Oxford, England, 1986. Springer-Verlag.

    Google Scholar 

  9. D. Kapur and G. Sivakumar. A total, ground path ordering for proving termination of ac-rewrite systems. In 8th InternationalConference on Rewriting Techniques and Applications, LNCS 1232, Sitges, Spain, 1997.

    Google Scholar 

  10. D. Kapur and G. Sivakumar. A recursive path ordering for proving associative-commutative termination, 1998.

    Google Scholar 

  11. D. Kapur, G. Sivakumar and H. Zhang. A new method for proving termination of ac-rewrite systems. In Conf. Found. of Soft. Technology and Theor. Comput. Science, LNCS 472, pp. 134–148, New Delhi, 1990. Springer-Verlag.

    Google Scholar 

  12. P. Narendran and M. Rusinowitch. Any ground associative commutative theory has a finite canonical system. In 4th Int. Conf. on Rewriting Techniques and Applications, LNCS 488, pp. 423–434, Como, 1991. Springer-Verlag.

    Google Scholar 

  13. A. Rubio and R. Nieuwenhuis. A total AC-compatible ordering based on RPO. Theoretical Computer Science, 142(2):209–227, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Rubio. A total AC-compatible ordering with RPO scheme. Technical Report UPC-LSI-97, Univ. Polit. Catalunya, September 1997.

    Google Scholar 

  15. A. Rubio. A fully syntactic AC-RPO. Technical Report UPC-LSI-98, Univ. Polit. Catalunya,December 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rubio, A. (1999). A Fully Syntactic AC-RPO. In: Narendran, P., Rusinowitch, M. (eds) Rewriting Techniques and Applications. RTA 1999. Lecture Notes in Computer Science, vol 1631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48685-2_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-48685-2_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66201-3

  • Online ISBN: 978-3-540-48685-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics