  Currently, memristor devices suffer from variability between devices and from
cycle to cycle. In this work, we study the impact of device variations on
memristive Material Implication (IMPLY). New constraints for different
parameters and variables are analytically derived and compared to extensive
simulation results, covering single gate and 1T1R crossbar structures. We show
that a static analysis based on switching conditions is not sufficient for an
overall assessment of robustness against device variability. Furthermore, we
outline parameter ranges within which the IMPLY gate is predicted to produce
correct output values. Our study shows that threshold voltage is the most
critical parameter. This work helps scientists and engineers to understand the
pitfalls of designing reliable IMPLY-based calculation units better and design
them with more ease. Moreover, these analyses can be used to determine whether
a certain memristor technology is suitable for implementation of IMPLY-based
circuits and systems.
