A polynomial-time algorithm for computing absolutely normal numbers

Authors:
Verónica Becher;Pablo Ariel Heiber;Theodore A. Slaman
Affiliations:
Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina and CONICET, Argentina;Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina;Department of Mathematics, University of California Berkeley, USA
Venue:
Information and Computation
Year:
2013

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Abstract

We give an algorithm to compute an absolutely normal number so that the first n digits in its binary expansion are obtained in time polynomial in n; in fact, just above quadratic. The algorithm uses combinatorial tools to control divergence from normality. Speed of computation is achieved at the sacrifice of speed of convergence to normality.