  Two approaches to studying the correlation functions of the binary Markov
sequences are considered. The first of them is based on the study of
probability of occurring different ''words'' in the sequence. The other one
uses recurrence relations for correlation functions. These methods are applied
for two important particular classes of the Markov chains. These classes
include the Markov chains with permutative conditional probability functions
and the additive Markov chains with the small memory functions. The exciting
property of the self-similarity (discovered in Phys. Rev. Lett. 90, 110601
(2003) for the additive Markov chain with the step-wise memory function) is
proved to be the intrinsic property of any permutative Markov chain.
Applicability of the correlation functions of the additive Markov chains with
the small memory functions to calculating the thermodynamic characteristics of
the classical Ising spin chain with long-range interaction is discussed.
