On a quantitative notion of uniformity

Extended abstract
  • Susanne Kaufmann
  • Martin Kummer
Contributed Papers Structural Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)


Recursive Function Recursive Tree Recursion Theory Total Selector Partial Recursive Function 
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  1. 1.
    R. Beigel, W. I. Gasarch, J. Gill, J. C. Owings, Jr. Terse, superterse, and verbose sets. Information and Computation, 103:68–85, 1993.CrossRefGoogle Scholar
  2. 2.
    R. Beigel, M. Kummer, F. Stephan. Quantifying the amount of verboseness. To appear in: Information and Computation. (A preliminary version appeared in: Lecture Notes in Computer Science, Vol. 620, pp. 21–32, 1992.)Google Scholar
  3. 3.
    A. Blumer, A. Ehrenfeucht, D. Haussler, M. K. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. Journal of the ACM, 36:929–966, 1989.CrossRefGoogle Scholar
  4. 4.
    J. Case, S. Kaufmann, E. Kinber, M. Kummer. Learning recursive functions from approximations. In: Proceedings of EuroCOLT'95. LNCS 904, 140–153, Springer-Verlag, 1995.Google Scholar
  5. 5.
    W. I. Gasarch. Bounded queries in recursion theory: a survey. In Proceedings of the Sixth Annual Structure in Complexity Theory Conference. IEEE Computer Society Press, 62–78, 1991.Google Scholar
  6. 6.
    V. Harizanov, M. Kummer, J. C. Owings, Jr. Frequency computation and the cardinality theorem. J. Symb. Log., 57:677–681, 1992.Google Scholar
  7. 7.
    C. G. Jockusch, R. I. Soare. Π10 classes and degrees of theories. Trans. Amer. Math. Soc., 173, 33–56, 1972.Google Scholar
  8. 8.
    S. Kaufmann. Uniformität bei rekursiv aufzählbaren Bäumen. Diplomarbeit, Fakultät für Informatik, Universität Karlsruhe, 1991.Google Scholar
  9. 9.
    E. B. Kinber. On frequency calculations of general recursive predicates. Sov. Math. Dokl., 13:873–876, 1972.Google Scholar
  10. 10.
    E. B. Kinber. Frequency-computable functions and frequency-enumerable sets. Candidate Dissertation, Riga, 1975. (in Russian)Google Scholar
  11. 11.
    M. Kummer. A proof of Beigel's cardinality conjecture. J. Symb. Log., 57:682–687, 1992.Google Scholar
  12. 12.
    M. Kummer, F. Stephan. Recursion theoretic properties of frequency computation and bounded queries. To appear in: Information and Computation. (A preliminary version appeared in: Lecture Notes in Computer Science, Vol. 713, pp. 243–254, 1993.)Google Scholar
  13. 13.
    D. W. Loveland. A variant of the Kolmogorov concept of complexity. In: Information and Control, 15:510–526, 1993.Google Scholar
  14. 14.
    P. Odifreddi. Classical Recursion Theory. North-Holland, Amsterdam, 1989.Google Scholar
  15. 15.
    J. C. Owings. A cardinality version of Beigel's nonspeedup theorem. J. Symb. Log., 54:761–767, 1989.Google Scholar
  16. 16.
    J. S. Royer, J. Case. Subrecursive Programming Systems: Complexity and Succinctness. Birkhäuser-Verlag, Boston, 1994.Google Scholar
  17. 17.
    R. I. Soare. Recursively Enumerable Sets and Degrees. Springer-Verlag, Berlin, 1987.Google Scholar
  18. 18.
    B. A. Trakhtenbrot. On frequency computation of functions. Algebra i Logika, 2:25–32, 1963. (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Susanne Kaufmann
    • 1
  • Martin Kummer
    • 1
  1. 1.Institut für Logik, Komplexität und DeduktionssystemeUniversität KarlsruheKarlsruheGermany

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