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Random generation of words of context-free languages according to the frequencies of letters

  • Alain Denise
  • Olivier Roques
  • Michel Termier
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Let L be a context-free language on an alphabet X={ x 1,x2,…, xk} and n a positive integer. We consider the problem of generating at random words of L with re-spect to a given distribution of the number of occurrences of the letters. We consider two alternatives of the problem. In the first one, a vector of natural numbers (n1, n2,…,nk) such that n1 + n2+… + nk = n is given, and the words must be generated uniformly among the set of words of L which contain exactly ni letters xi (1 ≤ i ≤ k). The second alternative consists, given v = (vi,…, vk) a vector of positive real numbers such that vi +… + vk = 1, to generate at random words among the whole set of words of L of length n, in such a way that the expected number of occurrences of any letter x i equals nvi (1 ≤i ≤ k), and two words having the same distribution of letters have the same probability to be generated. For this purpose, we design and study two alternatives of the recursive method which is classically employed for the uniform generation of combinatorial structures. This type of “controlled” non-uniform generation can be applied in the field of statistical analysis of genomic sequences.

Keywords

Random Generation Terminal Symbol Exact Frequency Discrete Apply Mathematic Rational Language 
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.

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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • Alain Denise
    • 1
  • Olivier Roques
    • 2
  • Michel Termier
    • 3
  1. 1.LRI, UMR CNRSUniversité Paris-Sud XIFrance
  2. 2.LaBRI, UMR CNRSUniversité Bordeaux IFrance
  3. 3.IGM, UMR CNRSUniversité Paris-Sud XIFrance

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