Constructivity, computability, and computational complexity in analysis

  • Klaus Weihrauch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 380)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Brouwer, L.E.J.: Historical background, principles, and methods of intuitionism, South African J.Sc. 49, 139–146 (1952)Google Scholar
  2. [2]
    Heyting, A.: Intuitionism, an introduction, North-Holland, Amsterdam, 1956 (revised 1972)Google Scholar
  3. [3]
    Troelstra, A.S.: Principles of intuitionism, Springer-Verlag, Berlin, Heidelberg, 1969Google Scholar
  4. [4]
    Bishop, E.; Bridges, D.S.: Constructive Analysis, Springer-Verlag, Berlin, Heidelberg, 1985Google Scholar
  5. [5]
    Ceitin, G.S.: Algorithmic operators in constructive complete separable metric spaces (in Russian), Doklady Akad, Nauk 128, 49–52 (1959)Google Scholar
  6. [6]
    Markov, A.A.: On constructive mathematics (in Russian), Trudy Mat. Inst. Stektov 67, 8–14 (1962)Google Scholar
  7. [7]
    Kushner, B.A.: Lectures on constructive mathematical logic and foundations of mathematics, Izdat. “Nauka”, Moscow, (1973)Google Scholar
  8. [8]
    Aberth, O.: Computable analysis, McGraw-Hill, New York, (1980)Google Scholar
  9. [9]
    Mazur, S.: Computable analysis, Rozprawy Matematyczne XXXIII (1963)Google Scholar
  10. [10]
    Grzegorczyk, A.: On the definition of computable real continuous functions, Fund.Math. 44, 61–71 (1957)Google Scholar
  11. [11]
    Mostowski, A.: On computable sequences, Fund.Math. 44, 37–51 (1955)Google Scholar
  12. [12]
    Lacombe, D.: Quelques procedes de definition en topologie recursive. In: Constructivity in mathematics (A. Heyting, ed.), North-Holland, Amsterdam,1959Google Scholar
  13. [13]
    Klaua, D.: Konstruktive Analysis, Deutscher Verlag der Wissenschaften, Berlin, 1961Google Scholar
  14. [14]
    Hauck, J.: Berechenbare reelle Funktionen, Zeitschrift f. math. Logik und Grdl. Math. 19, 121–140 (1973)Google Scholar
  15. [15]
    Scott, D.: Outline of a mathematical theory of computation Science, Proc. 4th Princeton Conference onInform. Sci., 1970Google Scholar
  16. [16]
    Brent, R.P.: Fast multiple precision evaluation of elementary functions, J. ACM 23, 242–251 (1976)CrossRefGoogle Scholar
  17. [17]
    Ko, K.; Friedman, H.: Computational complexity of real functions, Theoret. Comput. Sci. 20, 323–352 (1982)Google Scholar
  18. [18]
    Müller, N.Th.: Subpolynomial complexity classes of real functions and real numbers. In: Lecture notes in Computer Science 226, Springer-Verlag, Berlin, Heidelberg, 284–293, 1986Google Scholar
  19. [19]
    Müller, N.Th.: Uniform computational complexity of Taylor series. In: Lecture notes in Computer Science 267, Springer-Verlag, Berlin, Heidelberg, 435–444, 1987Google Scholar
  20. [20]
    Beeson, M.J.: Foundations of constructive mathematics, Springer-Verlag, Berlin, Heidelberg, 1985Google Scholar
  21. [21]
    Kreitz, Ch.; Weihrauch, K.: Compactness in constructive analysis revisited, Informatik-Berichte Nr. 49, Fernuniversität Hagen (1984) and Annals of Pure and Applied Logic 36, 29–38 (1987)Google Scholar
  22. [22]
    Kreitz, Ch.; Weihrauch, K.: A unified approach to constructive and recursive analysis. In: Computation and proof theory, (M.M. Richter et al., eds.), Springer-Verlag, Berlin, Heidelberg, 1984Google Scholar
  23. [23]
    Kreitz, Ch.; Weihrauch, K.: Theory of representations, Theoretical Computer Science 38, 35–53 (1985)CrossRefGoogle Scholar
  24. [24]
    Weihrauch, K.: Type 2 recursion theory, Theoretical Computer Science 38, 17–33 (1985)CrossRefGoogle Scholar
  25. [25]
    Weihrauch, K.; Kreitz, Ch.: Representations of the real numbers and of the open subsets of the set of real numbers, Annals of Pure and Applied Logic 35, 247–260 (1987)CrossRefGoogle Scholar
  26. [26]
    Weihrauch, K.: Computability, Springer-Verlag, Berlin, Heidelberg, 1987Google Scholar
  27. [27]
    Weihrauch, K.: On natural numberings and representations, Informatik-Berichte Nr.29, Fernuniversität Hagen, 1982Google Scholar
  28. [28]
    Weihrauch, K.; Kreitz, Ch.: Type 2 computational complexity of functions on Cantor's space (to appear)Google Scholar
  29. [29]
    Weihrauch, K.: Towards a general effectivity theory for computable metric spaces (to appear)Google Scholar
  30. [30]
    Weihrauch, K.: The complexity of online computations of real functions (in preparation)Google Scholar
  31. [31]
    Deil, Th.: Darstellungen und Berechenbarkeit reeller Zahlen, Informatik-Berichte Nr.51, Fernuniversität Hagen, 1984Google Scholar
  32. [32]
    Hinman, P.G.: Recursion-theoretic Hierachies, Springer-Verlag, Berlin, Heidelberg, 1978Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Klaus Weihrauch
    • 1
  1. 1.Theoretische Informatik, Fernuniversität DHagen

Personalised recommendations