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Complexity, Graphs, and the Dependency Pair Method

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5330))

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Abstract

This paper builds on recent efforts (Hirokawa and Moser, 2008) to exploit the dependency pair method for verifying feasible, i.e., polynomial runtime complexities of term rewrite systems automatically. We extend our earlier results by revisiting dependency graphs in the context of complexity analysis. The obtained new results are easy to implement and considerably extend the analytic power of our existing methods. The gain in power is even more significant when compared to existing methods that directly, i.e., without the use of transformations, induce feasible runtime complexities. We provide ample numerical data for assessing the viability of the method.

This research is partly supported by FWF (Austrian Science Fund) project P20133, Grant-in-Aid for Young Scientists 20800022 of the Ministry of Education, Culture, Sports, Science and Technology of Japan, and STARC.

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References

  1. Hirokawa, N., Moser, G.: Automated complexity analysis based on the dependency pair method. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195, pp. 364–379. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Lescanne, P.: Termination of rewrite systems by elementary interpretations. Formal Aspects of Computing 7(1), 77–90 (1995)

    Article  MATH  Google Scholar 

  3. Bonfante, G., Cichon, A., Marion, J.Y., Touzet, H.: Algorithms with polynomial interpretation termination proof. JFP 11(1), 33–53 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Avanzini, M., Moser, G.: Complexity analysis by rewriting. In: Garrigue, J., Hermenegildo, M.V. (eds.) FLOPS 2008. LNCS, vol. 4989, pp. 130–146. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Giesl, J., Arts, T., Ohlebusch, E.: Modular termination proofs for rewriting using dependency pairs. JSC 34(1), 21–58 (2002)

    MathSciNet  MATH  Google Scholar 

  8. Hirokawa, N., Middeldorp, A.: Tyrolean termination tool: Techniques and features. IC 205, 474–511 (2007)

    MathSciNet  MATH  Google Scholar 

  9. 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 

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

    Book  MATH  Google Scholar 

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

    Google Scholar 

  12. Hofbauer, D., Lautemann, C.: Termination proofs and the length of derivations. In: Dershowitz, N. (ed.) RTA 1989. LNCS, vol. 355, pp. 167–177. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  13. Contejean, E., Marché, C., Tomás, A.P., Urbain, X.: Mechanically proving termination using polynomial interpretations. JAR 34(4), 325–363 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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 

  15. Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. IC 199(1,2), 172–199 (2005)

    MathSciNet  MATH  Google Scholar 

  16. Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H.: SAT solving for termination analysis with polynomial interpretations. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 340–354. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, Japan

    Nao Hirokawa

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

    Georg Moser

Authors
  1. Nao Hirokawa
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  2. Georg Moser
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Editor information

Editors and Affiliations

  1. Carnegie Mellon University, Doha, Qatar

    Iliano Cervesato

  2. Technische Universität Darmstadt, Germany

    Helmut Veith

  3. University of Manchester, UK

    Andrei Voronkov

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Hirokawa, N., Moser, G. (2008). Complexity, Graphs, and the Dependency Pair Method. In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2008. Lecture Notes in Computer Science(), vol 5330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89439-1_45

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  • DOI: https://doi.org/10.1007/978-3-540-89439-1_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89438-4

  • Online ISBN: 978-3-540-89439-1

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