Small universal one-state linear operator algorithm

  • Frantisek Kascak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)


A one-state linear operator algorithm (OLOA) with modulus m, denned in the paper, operates with one non-negative integer x in the following manner. According to the value r=x MOD m either the computation is halted, or x is replaced by (ax+b) DIV c, where a,b,c are constants dependent only on the r, and the operation is repeated with the new value gained. The notion of a universal OLOA is defined, and a universal OLOA with modulus 396 is constructed in the paper.


Binary Relation Scheme Sign Partial Function Recursive Function Universal 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.


  1. 1.
    J. H. Conway, Unpredictable Iterations, Proc. 1972 Number Theory Conference, University of Colorado, Boulder, Colorado, 1972.Google Scholar
  2. 2.
    L. Gregusova, I. Korec, Small universal Minsky machine., Lecture Notes in Computer Science, vol. 74, Springer, 1979, pp. 308–316.Google Scholar
  3. 3.
    I. Korec, Introduction to Algorithms Theory, Comenius University, Bratislava, 1981, pp. 170. (Slovak)Google Scholar
  4. 4.
    A. I. Malcev, Algorithms and Recursive Functions., Nauka, Moscow, 1965, pp. 392. (Russian)Google Scholar
  5. 5.
    M. L. Minsky, Computation — Finite and Infinite Machines, Prentice Hall Inc., Englewood Cliffs, 1967.Google Scholar
  6. 6.
    H. Rogers, Theory of recursive functions and effective computability, McGraw-Hill Book Company, New York, 1967.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Frantisek Kascak
    • 1
  1. 1.Department of InformaticsSchool of EconomicsBanska BystricaCzechoslovakia

Personalised recommendations