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Pseudorandom numbers generated from shift register sequences

Part of the Lecture Notes in Mathematics book series (LNM,volume 1452)

Abstract

A survey of recent work on uniform pseudorandom numbers generated by the digital multistep and GFSR methods is presented. The emphasis is on the behavior of these pseudorandom numbers under tests for equidistribution and for statistical independence of successive pseudorandom numbers. A new general existence theorem for good parameters in the GFSR method is also shown.

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References

  1. D. A. André, G. L. Mullen, and H. Niederreiter: Figures of merit for digital multistep pseudorandom numbers, MATH. COMP., to appear.

    Google Scholar 

  2. J. Eichenauer, H. Grothe, and J. Lehn: Marsaglia's lattice test and non-linear congruential pseudo random number generators, METRIKA 35, 241–250 (1988).

    CrossRef  MATH  Google Scholar 

  3. J. Eichenauer and J. Lehn: A non-linear congruential pseudo random number generator, STATIST. HEFTE 27, 315–326 (1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. E. Hlawka: THEORIE DER GLEICHVERTEILUNG, Bibliographisches Institut, Mannheim, 1979.

    MATH  Google Scholar 

  5. D. E. Knuth: THE ART OF COMPUTER PROGRAMMING, Vol.2: SEMINUMERICAL ALGORITHMS, 2nd ed., Addison-Wesley, Reading, Mass., 1981.

    MATH  Google Scholar 

  6. L. Kuipers and H. Niederreiter: UNIFORM DISTRIBUTION OF SEQUENCES, Wiley, New York, 1974.

    MATH  Google Scholar 

  7. T. G. Lewis and W. H. Payne: Generalized feedback shift register pseudorandom number algorithm, J. ASSOC. COMPUT. MACH. 20, 456–468 (1973).

    CrossRef  MATH  Google Scholar 

  8. R. Lidl and H. Niederreiter: INTRODUCTION TO FINITE FIELDS AND THEIR APPLICATIONS, Cambridge Univ. Press, Cambridge, 1986.

    MATH  Google Scholar 

  9. G. L. Mullen and H. Niederreiter: Optimal characteristic polynomials for digital multistep pseudorandom numbers, COMPUTING 39, 155–163 (1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. H. Niederreiter: Quasi-Monte Carlo methods and pseudorandom numbers, BULL. AMER. MATH. SOC. 84, 957–1041 (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. H. Niederreiter: Applications des corps finis aux nombres pseudo-aléatoires, SÉM. THÉORIE DES NOMBRES 1982–1983, Exp. 38, Univ. de Bordeaux I, Talence, 1983.

    Google Scholar 

  12. H. Niederreiter: The performance of k-step pseudorandom number generators under the uniformity test, SIAM J. SCI. STATIST. COMPUTING 5, 798–810 (1984).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. H. Niederreiter: The serial test for pseudorandom numbers generated by the linear congruential method, NUMER. MATH. 46, 51–68 (1985).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. H. Niederreiter: Pseudozufallszahlen und die Theorie der Gleichverteilung, SITZUNGSBER. ÖSTERR. AKAD. WISS. MATH.-NATURWISS. KL. ABT. II 195, 109–138 (1986).

    MathSciNet  MATH  Google Scholar 

  15. H. Niederreiter: Rational functions with partial quotients of small degree in their continued fraction expansion, MONATSH. MATH. 103, 269–288 (1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. H. Niederreiter: A statistical analysis of generalized feedback shift register pseudorandom number generators, SIAM J. SCI. STATIST. COMPUTING 8, 1035–1051 (1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. H. Niederreiter: Point sets and sequences with small discrepancy, MONATSH. MATH. 104, 273–337 (1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. H. Niederreiter: The serial test for digital k-step pseudorandom numbers, MATH. J. OKAYAMA UNIV. 30, 93–119 (1988).

    MathSciNet  MATH  Google Scholar 

  19. R. C. Tausworthe: Random numbers generated by linear recurrence modulo two, MATH. COMP. 19, 201–209 (1965).

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. S. Tezuka: On the discrepancy of GFSR pseudorandom numbers, J. ASSOC. COMPUT. MACH. 34, 939–949 (1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. S. Tezuka: On optimal GFSR pseudorandom number generators, MATH. COMP. 50, 531–533 (1988).

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. A. van Wijngaarden: Mathematics and computing, PROC. SYMP. ON AUTOMATIC DIGITAL COMPUTATION (London, 1954), pp. 125–129, H.M. Stationery Office, London, 1954.

    Google Scholar 

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© 1990 Springer-Verlag

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Niederreiter, H. (1990). Pseudorandom numbers generated from shift register sequences. In: Hlawka, E., Tichy, R.F. (eds) Number-Theoretic Analysis. Lecture Notes in Mathematics, vol 1452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096988

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  • DOI: https://doi.org/10.1007/BFb0096988

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53408-2

  • Online ISBN: 978-3-540-46864-6

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