Recursively unsolvable algorithmic problems and related questions reexamined

  • Egon Börger
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 499)


Turing Machine Register Operator Recursive Function Combinatorial System Arbitrary Register 
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. AANDERAA, S. O. [1971]: On the decision problem for formulas in which all disjunctions are binary. in: Proc. Second Scand. Logic Symposium, Amsterdam 1971. pp. 1–18.Google Scholar
  2. Барэдинь, Я. М. [1963]: Об одном кпассе машин тяюинга (машины минского. in: АПГЕБРА и логика 1 (1963) 42–51.Google Scholar
  3. BÖRGER, E. [1971]: Reduktionstypen in Krom-und Hornformedin. Dissertation, Münster 1971.Google Scholar
  4. BÜCHI, J. R. [1962]: Turing-machines and the Entscheidungsproblem. in: Mathematische Annalen 148 (1962) 201–213.zbMATHMathSciNetCrossRefGoogle Scholar
  5. CHURCH, A. [1936]: A note on the Entscheidungsproblem. in: The Journal of Symbolic Logic 1 (1936) 40–41. Correction ibid. CHURCH, A. [1936]: A note on the Entscheidungsproblem. in: The Journal of Symbolic Logic 1 (1936) 101–102Google Scholar
  6. COHORS-FRESENBORG, E. [1973]: Berechenbare Funktionen und Registermaschinen —ein Beitrag zur Behandlung des Funktionsbegriffs auf konstruktiver Grundlage. in: Didaktik der Mathematik 3 (1973) 187–209.Google Scholar
  7. COHORS-FRESENBORG [1974]: Unentscheidbarkeitssätze in einem Leistungskurs “Grundlagen der Mathematik”. in: Beiträge zum Nathematikunterracht 1973, Hannover 1974, pp. 74–82.Google Scholar
  8. EILENBERG S. and ELGOT C. C. [1970]: Recursiveness. New York, 1970.Google Scholar
  9. GERMANO G. and MAGGIOLO-SCHETTINI A. [1973]: Quelques caractersations des fonctions récursives partielles. in: C. R. Acad. Sc. Paris, t. 276 (14 mai 1973), série A, pp. 1325–1327.zbMATHMathSciNetGoogle Scholar
  10. HERMES, H. [1965]: Enumerability, decidability, computability. Berlin et al. 1965.Google Scholar
  11. MALCEW, A. J. [1974]: Algorithmen und rekursive Funktionen. Braunschweig 1974.Google Scholar
  12. MARKOV, A. A. [1961]: Theory of algorithms. Israel Program for Scientific Translations 1961.Google Scholar
  13. MINSKY M. L. [1961]: Recursive unsolvability of Post's problem of “TAG” and other topics in theory of Turing machines. in: Annals of Math. 74 (1961) 437–455.zbMATHMathSciNetCrossRefGoogle Scholar
  14. MINSKY, M. L. [1967]: Computation: Finite and infinite machines. Englewood Cliffs 1967.Google Scholar
  15. OTTMANN, Th. [1974]: Rekursive Prozeduren und partiell rekursive Funktionen. Karlsruhe 1974, underground.Google Scholar
  16. POST, E. [1943]: Formal reductions of the combinatorial decision problem. in: Amer. J. Math. 65 (1943) 196–215.MathSciNetCrossRefGoogle Scholar
  17. PRIESE, L. [1971]: Normalformen von Markov'schen und Post'schen Algorithmen. Report, Institut für math. Logik und Grundlagenforschung of the University of Münster. pp. 124.Google Scholar
  18. RÖDDING, D. [1968]: Klassen rekursiver Funktionen. in: Proc. Summer School in Logic (Leeds 1967). Springer Lecture Notes in Math. Vol. 70, pp. 159–222.Google Scholar
  19. RÖDDING, D. [1972]: Registermaschinen. in: Der Mathematikunterricht 18 (1972) 32–41.Google Scholar
  20. RÖDDING, D. [1972a]: Einführung in die Theorie der berechenbaren Funktionen. Notes of lectures delivered at the Institut für math. Logik und Grundlagenforschung of the University of Münster, Summer 1972.Google Scholar
  21. ROGERS H., Jr. [1967]: Theory of recursive functions and effective computability. New York et al. 1967.Google Scholar
  22. SHEPHERDSON J. C. and STURGIS H. E. [1963]: Computability of recursive functions. in: J. Assoc. Comp. Mach. 10 (1963) 217–255.zbMATHMathSciNetGoogle Scholar
  23. TURING, A. M. [1936]: On computable numbers with an application to the Entscheidungsproblem. in: Proc. London Math. Soc. Ser. 2, 42 (1936) 230–265.zbMATHGoogle Scholar
  24. YASUHARA, A. [1971]: Recursive function theory and logic. New York, London 1971.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Egon Börger
    • 1
  1. 1.Istituto di Scienze dell'InformazioneUniversità di SalernoSalernoItaly

Personalised recommendations