Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity

  • Hugo Férée
  • Emmanuel Hainry
  • Mathieu Hoyrup
  • Romain Péchoux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6506)


We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These characterizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over the reals, a particular case of type 2 functions, and we provide a characterization of polynomial time complexity in Recursive Analysis.


Polynomial Time Turing Machine Order Polynomial Function Symbol Polynomial Time Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amadio, R.M.: Synthesis of max-plus quasi-interpretations. Fundamenta Informaticae 65(1), 29–60 (2005)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bellantoni, S., Cook, S.A.: A new recursion-theoretic characterization of the polytime functions. Computational complexity 2(2), 97–110 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bonfante, G., Marion, J.Y., Moyen, J.Y.: Quasi-interpretations. Theor. Comput. Sci. (to appear)Google Scholar
  4. 4.
    Cobham, A.: The Intrinsic Computational Difficulty of Functions. In: Logic, methodology and philosophy of science III, p. 24. North-Holland Pub. Co., Amsterdam (1965)Google Scholar
  5. 5.
    Constable, R.L.: Type two computational complexity. In: Proc. 5th annual ACM STOC, pp. 108–121 (1973)Google Scholar
  6. 6.
    Endrullis, J., Grabmayer, C., Hendriks, D., Isihara, A., Klop, J.W.: Productivity of stream definitions. Theor. Comput. Sci. 411(4-5), 765–782 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gaboardi, M., Péchoux, R.: Upper Bounds on Stream I/O Using Semantic Interpretations. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 271–286. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Irwin, R.J., Royer, J.S., Kapron, B.M.: On characterizations of the basic feasible functionals (Part I). J. Funct. Program. 11(1), 117–153 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Kapron, B.M., Cook, S.A.: A new characterization of type-2 feasibility. SIAM Journal on Computing 25(1), 117–132 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ko, K.I.: Complexity theory of real functions. Birkhauser Boston Inc., Cambridge (1991)CrossRefzbMATHGoogle Scholar
  11. 11.
    Lankford, D.: On proving term rewriting systems are noetherien. Tech. Rep. (1979)Google Scholar
  12. 12.
    Leivant, D., Marion, J.Y.: Lambda calculus characterizations of poly-time. In: Typed Lambda Calculi and Applications, pp. 274–288 (1993)Google Scholar
  13. 13.
    Manna, Z., Ness, S.: On the termination of Markov algorithms. In: Third Hawaii International Conference on System Science, pp. 789–792 (1970)Google Scholar
  14. 14.
    Mehlhorn, K.: Polynomial and abstract subrecursive classes. In: Proceedings of the Sixth Annual ACM Symposium on Theory of Computing, pp. 96–109. ACM, New York (1974)CrossRefGoogle Scholar
  15. 15.
    Ramyaa, R., Leivant, D.: Feasible functions over co-inductive data. In: WoLLIC, pp. 191–203 (2010)Google Scholar
  16. 16.
    Seth, A.: Turing machine characterizations of feasible functionals of all finite types. In: Feasible Mathematics II, pp. 407–428 (1995)Google Scholar
  17. 17.
    Weihrauch, K.: Computable analysis: an introduction. Springer, Heidelberg (2000)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hugo Férée
    • 1
  • Emmanuel Hainry
    • 2
    • 5
  • Mathieu Hoyrup
    • 3
    • 5
  • Romain Péchoux
    • 4
    • 5
  1. 1.ENS LyonLyon cedex 07France
  2. 2.Université Henri Poincaré, Nancy-UniversitéFrance
  3. 3.INRIA Nancy - Grand Est, Villers-lès-NancyFrance
  4. 4.Université Nancy 2, Nancy-UniversitéFrance
  5. 5.LORIAVandœuvre-lès-Nancy cedexFrance

Personalised recommendations