Abstract:
In the framework of the Kolmogorov approach to verifying the theory of probability an analysis of a result of S. S. Samarova on the length of the longest head-run for the Markov chain with two states is given. This result is a refinement and generalization of P. Erdös and P. Revesz's corresponding results. An analogous assertion is formulated and proved for individual random sequences. A complexity characterization of its application is also given.
Keywords:laws of large numbers, Markov chain, length of runs, individual random sequence, Kolmogorov complexity.
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