Synthesis of Symmetric Boolean Functions Using a Three-Stage Network

Abstract

This paper introduces a new three-stage circuit structure for synthesizing symmetric Boolean functions. The first stage of the proposed method improves upon an earlier approach to the synthesis of a special class of symmetric functions, known as matriochka symmetric functions. The second stage realizes the elementary symmetric functions from the matriochka symmetric functions of the first stage. Finally, in the third stage of the design, these elementary symmetric functions are used to synthesize any arbitrary symmetric function. Experiments on several benchmark functions show a reduction in circuit area compared to earlier results.