Construction of Recursive Algorithms for Polarity Matrices Calculation in Polynomial Logical Function Representation

 Dragan Jankovic 1

  Acta Cybernetica 14 (1999) 263-283.

Abstract:

 There is no algorithm for the calculation of optimal fixed polarity expansion. Therefore, the efficient calculation of polarity matrix consisting of all fixed polarity expansion coefficients is very important task. We show that polarity matrix can be generated as convolution of function f with rows of relates transform matrix. The recursive properties of the convolution matrix affect to properties of polarity matrix. In literature are known some recursive algorithms for the calculation of polarity matrix of some expressions for Multiple-valued (MV) functions [3,6]. We give a unique method to construct recursive procedures for the polarity matrices calculation for any Kronecker product based expression of MV functions. As a particular cases we derive two recursive algorithms for calculation of fixed polarity Reed-Muller-Fourier expressions for four-valued functions.  

Footnotes

  1  Faculty of Electronic Engineering, University of Nis, Yugoslavia