Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Deduction

CADE 2009: Automated Deduction – CADE-22 pp 339–354Cite as

Beyond Dependency Graphs

  • Conference paper

  • 620 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5663))

Abstract

The dependency pair framework is a powerful technique for proving termination of rewrite systems. One of the most frequently used methods within this framework is the dependency graph processor. In this paper we improve this processor by incorporating right-hand sides of forward closures. In combination with tree automata completion we obtain an efficient processor which can be used instead of the dependency graph approximations that are in common use in termination provers.

This is a preview of subscription content, 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   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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. TCS 236(1-2), 133–178 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  3. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2002), www.grappa.univ-lille3.fr/tata

  4. Dershowitz, N.: Termination of linear rewriting systems (preliminary version). In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 448–458. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  5. Durand, I., Middeldorp, A.: Decidable call-by-need computations in term rewriting. I&C 196(2), 95–126 (2005)

    MathSciNet  MATH  Google Scholar 

  6. Genet, T.: Decidable approximations of sets of descendants and sets of normal forms. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 151–165. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  7. Geser, A., Hofbauer, D., Waldmann, J., Zantema, H.: Finding finite automata that certify termination of string rewriting systems. IJFCS 16(3), 471–486 (2005)

    MathSciNet  MATH  Google Scholar 

  8. Geser, A., Hofbauer, D., Waldmann, J., Zantema, H.: On tree automata that certify termination of left-linear term rewriting systems. I&C 205(4), 512–534 (2007)

    MathSciNet  MATH  Google Scholar 

  9. Geupel, O.: Overlap closures and termination of term rewriting systems. Report MIP-8922, Universität Passau (1989)

    Google Scholar 

  10. Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic termination proofs in the dependency pair framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: Combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 301–331. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. JAR 37(3), 155–203 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. I&C 199(1-2), 172–199 (2005)

    MathSciNet  MATH  Google Scholar 

  15. Hirokawa, N., Middeldorp, A.: Tyrolean termination tool: Techniques and features. I&C 205(4), 474–511 (2007)

    MathSciNet  MATH  Google Scholar 

  16. Korp, M., Middeldorp, A.: Proving termination of rewrite systems using bounds. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 273–287. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Korp, M., Middeldorp, A.: Match-bounds with dependency pairs for proving termination of rewrite systems. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 321–332. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Korp, M., Middeldorp, A.: Match-bounds revisited. I&C (to appear, 2009)

    Google Scholar 

  19. Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean termination tool 2. In: Proc. 20th RTA. LNCS, vol. 5595, pp. 295–304. Springer, Heidelberg (2009)

    Google Scholar 

  20. Kusakari, K.: Termination, AC-Termination and Dependency Pairs of Term Rewriting Systems. PhD thesis, JAIST (2000)

    Google Scholar 

  21. Kusakari, K., Toyama, Y.: On proving AC-termination by AC-dependency pairs. Research Report IS-RR-98-0026F, School of Information Science, JAIST (1998)

    Google Scholar 

  22. Middeldorp, A.: Approximating dependency graphs using tree automata techniques. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 593–610. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  23. Middeldorp, A.: Approximations for strategies and termination. In: Proc. 2nd WRS. ENTCS, vol. 70, pp. 1–20 (2002)

    Google Scholar 

  24. Nagaya, T., Toyama, Y.: Decidability for left-linear growing term rewriting systems. I&C 178(2), 499–514 (2002)

    MathSciNet  MATH  Google Scholar 

  25. Thiemann, R.: The DP Framework for Proving Termination of Term Rewriting. PhD thesis, RWTH Aachen (2007); available as technical report AIB-2007-17

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Martin Korp & Aart Middeldorp

Authors
  1. Martin Korp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aart Middeldorp
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, The University of Manchester, Manchester, UK

    Renate A. Schmidt

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Korp, M., Middeldorp, A. (2009). Beyond Dependency Graphs. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02959-2_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02958-5

  • Online ISBN: 978-3-642-02959-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation