A recognition problem for a vector alphabet generating a sequence with a quasiperiodic structure

An off-line recognition problem is analyzed for a vector alphabet generating sequences with quasiperiodic vector fragments that coincide with alphabet vectors. It is shown that the solution of this problem reduces to solving a special optimization problem. It is proved that the problem considered is solvable in polynomial time, and an algorithm for its exact solution is justified. The algorithm ensures the maximum likelihood recognition of a vector alphabet for the case of additive noise which is a Gaussian sequence of independent random values having an identical distribution.