Study on Generalized Prefer-Opposite (GPO) Algorithm for Constructing the De Bruijn Binary Sequence

Abstract

De Bruijn binary sequence Sn of order n is a string of bits si ∈ {0,1} = {s1, …, s2 n}, so that each string with length n, {a 1, …, a n } ∈ {0,1}n appears exactly once. De Bruijn binary sequence can be built using the Generalized Prefer-Opposite (GPO) algorithm. The GPO algorithm is based on the Feedback Shift Register (FSR), which is a clock-regulated circuit with n sequential storage units. In running the algorithm, we need input consisting of the feedback function f(x 0,x 1, …, x n−1) and initial state b =b 0,b 1, …, b n−1 . There are many combinations of feedback functions and initial states that can be used, then grouped into three families namely family one, family two and family three. The purpose of this research is studying the GPO algorithm which use the feedback function from family two and initial state b =1100 in constructing the de Bruijn binary sequence. The result of this study indicate that the GPO algorithm with the feedback function and the initial state from the family two construct a de Bruijn binary sequence.