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Context-Free Grammars and Random Number Generation

  • Andrew C. Yao
Part of the NATO ASI Series book series (volume 12)

Abstract

In Monte Carlo calculations, one often needs to generate a random quantity X that satisfies certain (cumulative) distribution function F(x), i.e. Pr{Xx} = F(x). Numerous methods have been proposed for this purpose (see Ahrens and Dieter [1], Knuth [4]). An interesting question is: for a given F(x), how difficult is it to generate this distribution?

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References

  1. [1]
    Ahrens and Dieter Non-Uniform Random Numbers Wiley, New York, to appearGoogle Scholar
  2. [2]
    R. C. Gonzalez and M. G. Thomason, Syntactic Pattern Recognition, Addison-Wesley, Reading, Massachusetts, 1978.Google Scholar
  3. [3]
    J. E. Hoperoft and J. D. Ullman Introductin to Automata Theory Languages and Computation Addison-Wesley, Reading, Massachusetts, 1979Google Scholar
  4. [4]
    D. E. Knuth, The Art of Computer Programming, Vol.2, Addison-Wesley, Reading, Massachusetts, Second Edition, 1981.Google Scholar
  5. [5]
    D. E. Knuth and A. C. Yao, “The complexity of nonuniform random number generation,” in Algorithms and Complexity: New Directions and Recent Results, edited by J.F.Traub, Academic Press, New York, 1976, pp. 357–428.Google Scholar
  6. [6]
    Arto Salomaa and Matti Soittola Automata-Theoretic Aspects of Formal Power Series Springer-Verlag, New York, 1978Google Scholar
  7. [7]
    A. C. Yao, On generating nonuniform random numbers with a pushdown stack, Stanford Computer Science Department Technical Report, to appear, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Andrew C. Yao
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA

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