According to Kolmogorov, a finite object x is called ( alpha , beta )-stochastic, i. e. , it satisfies stochastic dependences, if there exists a finite set S such that x is an element of A, K(A) less than equivalent to alpha and K(x) greater than equivalent to log//2 vertical A vertical minus beta , where K is the simple Kolmogorov entropy (complexity), and vertical A vertical is the number of elements of set A. To define the concept of quasi-Kolmogorov stochasticity, the author examines the problem of the proportion of sequences that are not ( alpha , beta )-stochastic. The principal results are as follows: Upper and lower bounds are obtained for the a priori countable measure of all sequences of length n( greater than equivalent to n) that are not ( alpha , beta )-stochastic.
|Number of pages||7|
|Journal||Problems of information transmission|
|Publication status||Published - Apr 1985|