Recursive Threshold Logic - A Bioinspired Reconfigurable Dynamic Logic System with Crossbar Arrays

Abstract

The neuron behavioral models inspire from the principle of the firing of neurons, and weighted accumulation of charge for a given set of input stimuli. Biological neurons show dynamic behavior through its feedback and feedforward time-dependent responses. The principle of the firing of neurons inspires threshold logic design by applying threshold functions on the weight summation of inputs. We present a recursive threshold logic unit that uses the output feedback from standard threshold logic gates to emulate Boolean expressions in a time-sequenced manner. The Boolean expression is implemented with an analog resistive divider in memristive crossbars and a hard-threshold function designed with CMOS comparator for realizing the sums (OR) and products (AND) operators. The method benefits from reliable programming of the memristors in 1T1R crossbar configuration to suppress sneak path currents and thus enable larger crossbar sizes, which in turn allow a higher number of Boolean inputs. The reference threshold voltage for the decision comparators is tuned to implement AND and OR logic. The threshold value range is limited by the number of inputs to the crossbar. At the same time, the resistance of the memristors is kept constant at $R_{ON}$. The circuit's tolerance to the memristor variability and aging are analyzed, showing sufficient resilience. Also, the proposed recursive logic uses fewer cross-points, and has lower power dissipation than other memristive logic and CMOS implementation.