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The authors of the International Technology Roadmap for Semiconductors—the industry consensus set of goals established for advancing silicon integrated circuit technology—have challenged the computing research community to find new physical state variables (other than charge or voltage), new devices, and new architectures that offer memory and logic functions^,,,,, beyond those available with standard transistors. Recently, ultra-dense resistive memory arrays built from various two-terminal semiconductor or insulator thin film devices have been demonstrated^,,,,,. Among these, bipolar voltage-actuated switches have been identified as physical realizations of ‘memristors’ or memristive devices, combining the electrical properties of a memory element and a resistor^,. Such devices were first hypothesized by Chua in 1971 (ref. ), and are characterized by one or more state variables that define the resistance of the …