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Uniform approximation of continuous functions by probability functions of Boolean bases

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Abstract

Random Boolean expressions obtained by random and independent substitution of the constants 1, 0 with probabilities p, 1 − p, respectively, into random non-iterated formulas over a given basis are considered. The limit of the probability of appearance of expressions with the value 1 under unrestricted growth of the complexity of expressions, which is called the probability function, is considered. It is shown that for an arbitrary continuous function f(p) mapping the segment [0, 1] into itself there exists a sequence of bases whose probability functions uniformly approximate the function f(p) on the segment [0, 1].

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References

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    A. D. Yashunskii

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  1. A. D. Yashunskii
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Additional information

Original Russian Text © A.D. Yashwnskii, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 2, pp. 37–43.

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Yashunskii, A.D. Uniform approximation of continuous functions by probability functions of Boolean bases. Moscow Univ. Math. Bull. 62, 78–84 (2007). https://doi.org/10.3103/S0027132207020064

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  • DOI: https://doi.org/10.3103/S0027132207020064

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