Indices of regularity and indices of randomness for m-ary strings

Abstract

The notions “regularity index” and “randomness index” previously introduced forbinary 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 These notions are complementary and the regular/random dichotomyhas been replaced by a gradation of values of regularity and of randomness.With this approach, the more regular an m-ary string, the less random it is, and viceversa. The distributions of frequencies of different length strings —2-ary and 3-arystrings— according to their indices of randomness, are shown by histograms.Keywords: regularity index, randomness index, m-ary strings.Las nociones de ´?ndice de regularidad y de ´?ndice de aleatoriedad previamente introducidaspara cadenas binarias (2-arias) son modificadas ligeramente y generalizadaspara cadenas m-arias (m = 2, 3, 4, . . .). Dichas nociones resultan complementarias y ladicotom´?a regular-aleatorio es sustituida por una gradaci´on de valores de regularidady de aleatoriedad. Con el enfoque utilizado, cuanto m´as regular es una cadena m-ariamenos aleatoria debe ser considerada y viceversa. Las distribuciones de frecuenciasde cadenas —de diversas longitudes— 2-arias y 3-arias en funci´on de sus ´?ndices dealeatoriedad son presentadas mediante histogramas.Palabras clave: ´?ndice de regularidad, ´?ndice de aleatoriedad, cadenas m-arias.