An Improved Approach for the Synthesis of Boolean Functions Using Memristor Based IMPLY and INVERSE-IMPLY Gates

Research on memristors have drawn wide attention in recent years as these devices exhibit unique properties which can be used to perform various logic and memory operations. Memristor based memory systems are expected to replace flash memory devices in the near future. In addition, synthesis and optimization of boolean functions using memristors are becoming an important area of research. There are various logic design styles for memristors that have been reported, among which the one that implements material implication operation forms the basis of the present work. An IMPLY gate implements the implication operation, and can be realized using only two memristors and one resistance. In the present work, the widely available synthesis tool ABC is used for synthesizing an arbitrary boolean function into a netlist of IMPLY gates. To optimize the number of memristors to be used for the realization, we propose an INVERSE-IMPLY gate for handling fanouts in the intermediate netlist generated by the ABC tool. Synthesis experiments have been carried out on standard benchmark functions of up to 16 variables, which show an overall improvement of 22.8% in the number of steps required for evaluation over an existing stateof-the-art method. For functions with 9 or more variables, the improvement increases to 35.5%.