Exploring factored forms for sequential implication logic synthesis

Abstract

This work proposes the use of non-recursive factored forms in material implication logic as a way to increase performance with a small additional cost in the number of required devices. Previous works addressing memristor based implication logic focus only on recursive forms. The utilization of factored forms can reduce the number of operations. Since this kind of logic is naturally sequential, the number of operations is direct related to the computation time. However, additional devices may be needed. Considering all Boolean functions up to 4 inputs, the average reduction in the number of implications when using factored forms instead of recursive forms is 8%. The best case of reduction obtained was 60% by adding only one extra memristor.