Logical not polynomial forms to represent multiple-valued functions

The synthesis of logical not polynomial forms to represent completely and incompletely defined multiple-valued logic functions is proposed. To compute these forms, discrete orthogonal transforms are used. The matrix and vector procedures are the foundation of the logic not polynomial form synthesis to represent multiple -valued functions. The main advantage of this forms is the possibility to investigate the properties of multiple-valued logical functions and to use the implementation of fast discrete orthogonal transforms for computation of analytical description coefficients. Genetic algorithms are applied to synthesize incompletely defined multiple valued functions.