About the distribution of the numbers of pairs and triples of equal signs in a cycle of binary multicyclic sequence

The article presents the limit distribution of the numbers of pairs and triples of equal signs in a cycle of binary multicyclic random sequence with registers filled with uniform distributed mutually independent binary random variables in two cases: 1) when the number of registers is fixed and their lengths tend to infinity; 2) when it also tends to infinity. In the first case using the Berry-Esseen inequality we have derived the uniform estimates of the degree of convergence.