Construction of Digital Logic Systems based on the GFDD

This paper propose the design method of the constructing the digital logic systems over galois fields using by the galois field decision diagram(GFDD) that is based on the graph theory. The proposed design method is as following. First of all, we discuss the mathematical properties of the galois fields and the basic properties of the graph theory. After we discuss the operational domain and the functional domain, we obtain the transformation matrixes, $\psi$GF(P)(1) and $\xi$GF(P)(1), in the case of one variable, that easily manipulate the relationship between two domains. And we extend above transformation matrixes to n-variable case, we obtain $\psi$GF(P)(1) and $\xi$GF(P)(1). We discuss the Reed-Muller expansion in order to obtain the digital switching functions of the P-valued single variable. And for the purpose of the extend above Reed-Muller expansion to more two variables, we describe the Kronecker product arithmetic operation.

GFDD에 기초한 디지털논리시스템 구성

본 논문에서는 그래프 이론에 기초를 둔 GFDD를 사용하여 디지털논리시스템을 구성하는 한가지 방법을 제안하였다. 제안한 방법은 먼저 유한체와 그래프 이론의 수학적 성질을 논의하였으며, 단일변수에 대한 동작영역과 함수영역간의 변환을 용이하게 하기 위한 변환행렬 $\psi$GF(P)(1)과 $\xi$GF(P)(1)을 논의하였다. 그리고 디지털스위칭함수를 구하기 위한 Reed-Muller 확장을 논의하였으며, 이를 다변수인 경우로 확장하기 위해 Kronecker Product를 논의하였다.