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Polynomial Interpretations with Negative Coefficients

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Book cover Artificial Intelligence and Symbolic Computation (AISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3249))

Abstract

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x–1 for a unary function symbol or x–y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating.

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References

  1. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-09, RWTH Aachen (2001)

    Google Scholar 

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

    Google Scholar 

  4. Ben Cherifa, A., Lescanne, P.: Termination of rewriting systems by polynomial interpretations and its implementation. Science of Computer Programming 9, 137–159 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Contejean, E., Marché, C., Monate, B., Urbain, X.: CiME version 2 (2000), Available at http://cime.lri.fr/

  6. Contejean, E., Marché, C., Tomás, A.-P., Urbain, X.: Mechanically proving termination using polynomial interpretations. Research Report 1382, LRI (2004)

    Google Scholar 

  7. Dershowitz, N.: 33 Examples of termination. In: Comon, H., Jouannaud, J.-P. (eds.) TCS School 1993. LNCS, vol. 909, pp. 16–26. Springer, Heidelberg (1995)

    Google Scholar 

  8. Dershowitz, N., Hoot, C.: Natural termination. Theoretical Computer Science 142(2), 179–207 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Giesl, J.: Generating polynomial orderings for termination proofs. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 426–431. Springer, Heidelberg (1995)

    Google Scholar 

  10. Giesl, J., Arts, T., Ohlebusch, E.: Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation 34(1), 21–58 (2002)

    Article  MathSciNet  Google Scholar 

  11. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated termination proofs with AProVE. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 210–220. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 32–46. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Hirokawa, N., Middeldorp, A.: Tyrolean termination tool. In: Proc. 7th Internation Workshop on Termination, Technical Report AIB-2004-07, RWTH Aachen, pp. 59–62 (2004)

    Google Scholar 

  15. Hong, H., Jakuš, D.: Testing positiveness of polynomials. Journal of Automated Reasoning 21, 23–28 (1998)

    Article  MathSciNet  Google Scholar 

  16. Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)

    Google Scholar 

  17. Lucas, S.: Polynomials for proving termination of context-sensitive rewriting. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 318–332. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Lucas, S.: Polynomials over the reals in proof of termination. In: Proc. 7th Internation Workshop on Termination, Technical Report AIB-2004-07, RWTH Aachen, pp. 39–42 (2004)

    Google Scholar 

  19. Steinbach, J.: Generating polynomial orderings. Information Processing Letters 49, 85–93 (1994)

    Article  MATH  Google Scholar 

  20. Steinbach, J., Kühler, U.: Check your ordering – termination proofs and open problems. Technical Report SR-90-25, Universität Kaiserslautern (1990)

    Google Scholar 

  21. Terese. Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  22. Thiemann, R., Giesl, J., Schneider-Kamp, P.: Improved modular termination proofs using dependency pairs. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 75–90. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  23. Urbain, X.: Modular & incremental automated termination proofs. Journal of Automated Reasoning (2004) (to appear)

    Google Scholar 

  24. Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24, 89–105 (1995)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, 6020, Innsbruck, Austria

    Nao Hirokawa & Aart Middeldorp

Authors
  1. Nao Hirokawa
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  2. Aart Middeldorp
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Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

    Bruno Buchberger

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    John Campbell

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Hirokawa, N., Middeldorp, A. (2004). Polynomial Interpretations with Negative Coefficients. In: Buchberger, B., Campbell, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2004. Lecture Notes in Computer Science(), vol 3249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30210-0_16

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  • DOI: https://doi.org/10.1007/978-3-540-30210-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23212-4

  • Online ISBN: 978-3-540-30210-0

  • eBook Packages: Springer Book Archive

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