One Optimization Problem Induced by the Segregation Problem for the Sum of Two Quasiperiodic Sequences

An unexplored discrete optimization problem of summing the elements of three given numerical sequences is considered. This problem is a core, within the framework of a posteriori approach, of the noise-proof segregation problem for two independent unobservable quasiperiodic sequences, i.e., the sequences that include some non-intersecting subsequences-fragments having the predetermined characteristic properties with the limitations from below and above on the interval between two successive fragments. The segregation problem is to restore the unobservable sequences on the base of their noisy sum. In the current paper, all the fragments in a single sequence are assumed to be identical and coinciding with the given reference fragment, at that, the information about the number of fragments in it is unavailable. It is shown constructively that, despite the exponentially-sized set of possible solutions to the optimization problem under consideration, as well as in the segregation problem, both these problems are polynomially solvable. Some numerical simulation results are given for illustration.