On one recognition problem of vector alphabet generating a sequence with a quasi-periodical structure

In this paper, we analyze one version of the off-line recognition problem of the vector alphabet in the case when this alphabet is a generator of sequences having quasi-periodical vector-fragments, these fragments coinciding with alphabet vectors. It is shown that the solution of this problem is reduced to that of a special optimization problem. We have proven that this problem is solvable in a polynomial time. An algorithm for an exact solution to this problem is justified. This algorithm ensures the maximum-likelihood recognition of the vector alphabet under condition when the noise is additive and is a Gaussian sequence of independent random values having an identical distribution.