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The objective of our research is to create efficient methods and tools for the quick and thorough assessment of emerging digital circuit devices, facilitating the adoption of promising ones. In this work, we develop methods and tools for hybrid technology that combines memristors with MOS transistors and demonstrates their effectiveness. Although several types of memristor-transistor logic have been proposed, 15 years of research has created a small set of logic cells. We propose a systematic method for generating new and efficient memristor-transistor single-phase combinational logic cells. At the core of our approach is a cell enumerator, which enables us to explore a wide range of cell designs, including nonintuitive ones, and a data-driven inductive learning method, which identifies new properties of such cells and scales up our explorations. In conjunction with other completely new tools, these create a comprehensive and definitive library of logic cells. Our new cells provide significant improvements or significantly distinct Pareto-optimal alternatives for the few logic functions for which prior research has created cells. Importantly, our methods enable us to discover a previously unknown synergistic operation between memristors and transistors that occurs for specific cell topologies. We harness this synergy to develop a method for adding memristors to low-area pass-transistor circuits such that they produce strong output voltages and low power, including for patterns that cause ratioed operation. We have also developed a new memristor-transistor logic family, namely controlled-AND (cAND)/controlled-OR (cOR), which includes many of the best cells. We have also developed a constructive method for designing such cells.