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

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 These notions are complementary and the regular/random dichotomy has been replaced by a gradation of values of regularity and of randomness.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. Keywords: regularity index, randomness index, m-ary strings.