On finite and infinite computations

  • A. Kreczmar
Section C Computability, Decidability & Arithmetic Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 56)


In the present paper we shall try to characterize the properties of programmable functions and relations over some relational structures. The structures which constitute the major part of our investigations are the fields of real and complex numbers. We shall deal with some general questions concerning the elimination of while-statements. It will be shown that this elimination is possible for a wide class of programs over fields which satisfy a certain algebraic condition.


Algebraic Varie Recursive Function Programmable Function Open Formula Partial Recursive Function 
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.

6. References

  1. 1.
    E. Engeler, Algorithmic properties of structures, Math. Sys. Th. 1 (1967)Google Scholar
  2. 2.
    N. Jacobson, Lectures in abstract algebra, Van. Nost. Comp. (1951)Google Scholar
  3. 3.
    D. Kfoury, Comparing algebraic structures up to algorithmic equivalence, Proc. Ist Coll. Aut. Lan. Prog., North Holl. (1972)Google Scholar
  4. 4.
    A. Kreczmar, On infinite sets of polynomial relations, Bul. Acad. Pol. Sc. Ser. Astr. Math. Phys. 25 (1977)Google Scholar
  5. 5.
    A. Kreczmar, Programmability in fields, Fundam. Infor. /to appear/Google Scholar
  6. 6.
    H. Rogers, Jr., Theory of recursive functions and effective computability, McGraw-Hill Comp., (1967)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • A. Kreczmar
    • 1
  1. 1.University of WarsawPoland

Personalised recommendations