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Small universal one-state linear operator algorithm

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Mathematical Foundations of Computer Science 1992 (MFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 629))

Abstract

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.

I would like to thank Ivan Korec for many helpful discussions concerning this work.

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References

  1. J. H. Conway, Unpredictable Iterations, Proc. 1972 Number Theory Conference, University of Colorado, Boulder, Colorado, 1972.

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  2. L. Gregusova, I. Korec, Small universal Minsky machine., Lecture Notes in Computer Science, vol. 74, Springer, 1979, pp. 308–316.

    Google Scholar 

  3. I. Korec, Introduction to Algorithms Theory, Comenius University, Bratislava, 1981, pp. 170. (Slovak)

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  4. A. I. Malcev, Algorithms and Recursive Functions., Nauka, Moscow, 1965, pp. 392. (Russian)

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  5. M. L. Minsky, Computation — Finite and Infinite Machines, Prentice Hall Inc., Englewood Cliffs, 1967.

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  6. H. Rogers, Theory of recursive functions and effective computability, McGraw-Hill Book Company, New York, 1967.

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Authors and Affiliations

  1. Department of Informatics, School of Economics, Tajovskeho 10, 975 90, Banska Bystrica, Czechoslovakia

    Frantisek Kascak

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  1. Frantisek Kascak
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Ivan M. Havel Václav Koubek

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© 1992 Springer-Verlag Berlin Heidelberg

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Kascak, F. (1992). Small universal one-state linear operator algorithm. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55808-X_31

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  • DOI: https://doi.org/10.1007/3-540-55808-X_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55808-8

  • Online ISBN: 978-3-540-47291-9

  • eBook Packages: Springer Book Archive

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