Logic functions representation and synthesis of k-valued digital circuits in linear algebra

The mathematical basics of the non-classical approach to the logical synthesis of k-valued digital structures based on the replacement of the classic mathematical apparatus of logic synthesis (Boolean algebra) to the proposed mathematical apparatus - linear algebra are considered. The logic synthesis process of two valued and multi-valued digital structures in linear algebra including the formation of bases of a linear space and original representation of the implemented logical function are discussed. Mathematical advantages of the proposed approach, which could be the basis for designing of high-speed digital logic structures for various applications are considered.