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The conditional switching of memristors to execute stateful implication logic is an example of in-memory computation to potentially provide high energy efficiency and improved computation speed by avoiding the movement of data back and forth between a processing chip and memory and/or storage. Since the first demonstration of memristor implication logic, a significant goal has been to improve the logic cascading to make it more practical. Here, we describe and experimentally demonstrate nine symmetry-related Boolean logic operations by controlling conventional Ta/TaOx/Pt memristors integrated in a crossbar array with applied voltage pulses to perform conditional SET or RESET switching involving two or three devices, i.e., a particular device is switched depending on the state of another device. We introduce a family of four stateful two-memristor logic gates along with the copy and negation operations that enable two-input-one-output complete logic. In addition, we reveal five stateful three-memristor gates that eliminate the need for a separate data copy operation, decreasing the number of steps required for a particular task. The diversity of gates made available by simply applying coordinated sequences of voltages to a memristor crossbar memory significantly improves stateful logic computing efficiency compared to similar approaches that have been proposed.

A Family of Stateful Memristor Gates for Complete Cascading Logic