Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://www.revistas.ucr.ac.cr/index.php/matematica/oai
Indices of regularity and indices of randomness for m-ary strings
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Keywords

regularity index
randomness index
m-ary strings
ı́ndice de regularidad
ı́ndice de aleatoriedad
cadenas m-arias

How to Cite

Skliar, O., Monge, R. E., Oviedo, G., & Medina, V. (2009). Indices of regularity and indices of randomness for m-ary strings. Revista De Matemática: Teoría Y Aplicaciones, 16(1), 43–59. https://doi.org/10.15517/rmta.v16i1.1418

Abstract

The notions “regularity index” and “randomness index” previously introduced for binary strings (2-ary) have been modified slightly and generalized for m-ary strings (m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomy has been replaced by a gradation of values of regularity and of randomness. With this approach, the more regular an m-ary string, the less random it is, and vice versa. The distributions of frequencies of different length strings —2-ary and 3-ary strings— according to their indices of randomness, are shown by histograms.

https://doi.org/10.15517/rmta.v16i1.1418
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References

Chaitin G.J. (1998) The Limits of Mathematics. Springer-Verlag, New York.

Chaitin, G.J. (2001) Exploring Randomness. Springer-Verlag, New York.

Pincus, S.; Singer, B. H. (1996) “Randomness and degrees of irregularity”, Proceedings of the National Academy of Scienes of the United States of America 93(5): 2083–2088.

Skliar, O.; Medina, V.; Oviedo G. (1995) “Un ı́ndice de aleatoriedad para cadenas binarias”, in: J. Trejos (Ed.) Memorias del IX Simposio Métodos Matemáticos Aplicados en las Ciencias, Turrialba: 161–172.

Volchan, S.B. (2002) “What is a random sequence?”, The American Mathematical Monthly 109(1): 46–63.

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