Prediction of Solutions of Arithmetic and Logical Operations on the Basis of the Mathematical Model of Cognitive Digital Automata

An approach to the problem of solution prediction of arithmetic and logical operations on the basis of the mathematical model of cognitive digital automata (CDA) is proposed. A particular advantage of the proposed approach is that the training procedure can be performed on limited (minimum) training sets. Prediction or generation of solutions is performed on the basis of the mathematical model of CDA which is formed in the course of training. As a testbed for the approach, the modeling of an n-bit parallel adder was implemented. The mathematical model of the adder was formed, which made it possible to reproduce the entire truth table for the n-bit parallel adder. The results obtained could be useful as an alternative solution to a number of problems known for conventional feed-forward neural networks, e.g. on-the-fly learning and catastrophic forgetting.