Multi-valued and Fuzzy Logic Realization using TaOx Memristive Devices

Vikas Rana,Anupam Chattopadhyay,Rainer Waser,Wonjoo Kim,Debjyoti Bhattacharjee

doi:10.1038/s41598-017-18329-3

Abstract

Among emerging non-volatile storage technologies, redox-based resistive switching Random Access Memory (ReRAM) is a prominent one. The realization of Boolean logic functionalities using ReRAM adds an extra edge to this technology. Recently, 7-state ReRAM devices were used to realize ternary arithmetic circuits, which opens up the computing space beyond traditional binary values. In this manuscript, we report realization of multi-valued and fuzzy logic operators with a representative application using ReRAM devices. Multi-valued logic (MVL), such as Łukasiewicz logic generalizes Boolean logic by allowing more than two truth values. MVL also permits operations on fuzzy sets, where, in contrast to standard crisp logic, an element is permitted to have a degree of membership to a given set. Fuzzy operations generally model human reasoning better than Boolean logic operations, which is predominant in current computing technologies. When the available information for the modelling of a system is imprecise and incomplete, fuzzy logic provides an excellent framework for the system design. Practical applications of fuzzy logic include, industrial control systems, robotics, and in general, design of expert systems through knowledge-based reasoning. Our experimental results show, for the first time, that it is possible to model fuzzy logic natively using multi-state memristive devices.

Highlights

In 300 BC, Aristotle proposed the principle of non-contradiction which ruled out simultaneous existence of two contradictory propositions[3]
Equal stepping of operand voltages is enabled using an OFFSET voltage VOFFSET = 0.7V. (a) Keeping the VBE = 0.7V constant, VTE is varied from −0.7V to −1.5V in steps of −0.2V i.e. Vv = 0V and Vu = 0, 0.2, ..., 0.8V. (b) The corresponding resistance levels R0, ..., R4 states are programmed to the device
Fuzzy set allows its elements with certain degrees of membership, in contrast to a crisp set

Summary

Introduction

In 300 BC, Aristotle proposed the principle of non-contradiction which ruled out simultaneous existence of two contradictory propositions[3]. Further applications of fuzzy logic include expert systems[14], robotics[15] and diverse sub-domains of machine intelligence[16] Despite these wide ranging applications of MVL, the present computing technology is heavily based on Boolean logic. A limiting factor of MVL realization has been the inherent representation of information in binary format in semiconductor devices, thereby forcing a designer to switch between logic formats, which was clearly an inefficient solution In this manuscript, we leverage the multi-state memristive devices which can inherently operate in the multi-valued domain. ReRAM based passive crossbar arrays offer the implementation of memory-intensive computing paradigms, i.e. the logic operations are directly processed in the memory and arithmetic tasks. Memristive crossbar arrays can enable the multi-parallel search algorithms for pattern recognition tasks, widely required for neuromorphic applications[30]

Methods

Results

Discussion

Conclusion