International Conference on Rewriting Techniques and Applications

RTA 2014: Rewriting and Typed Lambda Calculi pp 179-193 | Cite as

An Implicit Characterization of the Polynomial-Time Decidable Sets by Cons-Free Rewriting

  • Daniel de Carvalho
  • Jakob Grue Simonsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8560)

Abstract

We define the class of constrained cons-free rewriting systems and show that this class characterizes P, the set of languages decidable in polynomial time on a deterministic Turing machine. The main novelty of the characterization is that it allows very liberal properties of term rewriting, in particular non-deterministic evaluation: no reduction strategy is enforced, and systems are allowed to be non-confluent.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jones, N.D.: Logspace and ptime characterized by programming languages. Theor. Comput. Sci. 228(1-2), 151–174 (1999)CrossRefMATHGoogle Scholar
  2. 2.
    Bonfante, G.: Some programming languages for logspace and ptime. In: Johnson, M., Vene, V. (eds.) AMAST 2006. LNCS, vol. 4019, pp. 66–80. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Jones, N.D.: The expressive power of higher-order types or, life without cons. J. Funct. Program. 11(1), 5–94 (2001)CrossRefGoogle Scholar
  4. 4.
    Avanzini, M., Moser, G.: Closing the gap between runtime complexity and polytime computability. In: Lynch, C. (ed.) RTA. LIPIcs, vol. 6, pp. 33–48. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)Google Scholar
  5. 5.
    Hofmann, M.: Type systems for polynomial-time computation. Habilitationsschrift (1999)Google Scholar
  6. 6.
    Bellantoni, S., Cook, S.A.: A new recursion-theoretic characterization of the polytime functions. Computational Complexity 2, 97–110 (1992)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Bellantoni, S.J., Niggl, K.H., Schwichtenberg, H.: Higher type recursion, ramification and polynomial time. Ann. Pure Appl. Logic 104(1-3), 17–30 (2000)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Baillot, P., Lago, U.D.: Higher-Order Interpretations and Program Complexity. In: Cégielski, P., Durand, A. (eds.) Computer Science Logic (CSL 2012). Leibniz International Proceedings in Informatics (LIPIcs), vol. 16, pp. 62–76. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl (2012)Google Scholar
  9. 9.
    Baillot, P.: From proof-nets to linear logic type systems for polynomial time computing. In: Ronchi Della Rocca, S. (ed.) TLCA 2007. LNCS, vol. 4583, pp. 2–7. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Baillot, P., Gaboardi, M., Mogbil, V.: A polytime functional language from light linear logic. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 104–124. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Avanzini, M., Eguchi, N., Moser, G.: A new order-theoretic characterisation of the polytime computable functions. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 280–295. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Avanzini, M., Moser, G.: Polynomial path orders. Logical Methods in Computer Science 9(4) (2013)Google Scholar
  13. 13.
    Goerdt, A.: Characterizing complexity classes by general recursive definitions in higher types. Inf. Comput. 101(2), 202–218 (1992)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Goerdt, A.: Characterizing complexity classes by higher type primitive recursive definitions. Theor. Comput. Sci. 100(1), 45–66 (1992)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Kristiansen, L., Niggl, K.H.: On the computational complexity of imperative programming languages. Theor. Comput. Sci. 318(1-2), 139–161 (2004)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Terese (ed.): Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press (2003)Google Scholar
  17. 17.
    Jones, N.D.: Computability and complexity: from a programming perspective. The MIT Press (1997)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daniel de Carvalho
    • 1
  • Jakob Grue Simonsen
    • 1
  1. 1.Department of Computer ScienceUniversity of Copenhagen (DIKU)Copenhagen SDenmark

Personalised recommendations