For a computable probability distribution P over the set of infinite binary sequences Martin-Löf defined a test d(x|P) measuring the degree of nonrandomness of the sequence x with respect of P. We give some expressions in terms of Kolmogorov's and other complexities of the initial segments of x whose difference from d(x|P) is bounded by a constant.
CITATION STYLE
Gács, P. (1979). Exact expressions for some randomness tests. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 67 LNCS, pp. 124–131). Springer Verlag. https://doi.org/10.1007/3-540-09118-1_14
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