The classical pattern recognition problems are considered. A model of learning Boolean formulas is implemented. Computational procedures for constructing non-reducible descriptors and clusters are brieey discussed. Possible applications of non-reducible de-scriptors to ECG analysis and ECG recognition are suggested.

B. Liu has recently obtained the maximum value for the kth upper multiexponents of primitive, nearly reducible matrices of order n with 1 ≤ k ≤ n. In this paper primitive, nearly reducible matrices whose kth upper multiexponents attain the maximum value are completely characterized.