Minimization of Quaternary Galois Field Sum of Products Expression for Multi-Output Quaternary Logic Function Using Quaternary Galois Field Decision Diagram

Abstract

A quaternary logic function expressed as quaternary Galois field sum of products (QGFSOP) expression can be realized as a cascade of quaternary 1-qudit, Feynman, and Toffoli gates. In this paper, we have presented a heuristic algorithm for simultaneous variable ordering and quaternary Galois field expansion selection for constructing optimal quaternary Galois field decision diagram (QGFDD). We have also shown the way of flattening the QGFDD for generating QGFSOP expression. We have written Java program to construct QGFDD for multi-output quaternary functions and provided experimental results.