Spectral analysis and synthesis of logical functions for special-purpose VLSI implementation

Some results of investigation into the spectral properties of k-valued (k ≥ 2) logical functions are presented. The main goal of the investigation is to show the power of spectral methods in implicant extraction and recognition of some useful logical function properties. The relation between the sum-of-products form of a logical function and its spectrum is established by means of a group representation of implicants. It allowed to attract some results of abstract harmonic analysis of discrete-valued functions. A number of theorems which states the necessary and sufficient conditions for the existence or absence of an implicant and for recognition of monotonicity and symmetry are formulated. The application of the results is shown by presenting an algorithm for deriving an irredundant sum-of-product form of a logical function.