We present a new approach for early analysis of logic gates that is based on formal methods. As device technology research takes years and is very expensive, it is desirable to evaluate a technology's potential as early as possible, which is hard to do with current techniques. The actual impact of new devices on circuit design and their performance in complex circuits, are difficult to predict using simulation-based techniques. We propose a new approach that supplements simulation-based analysis and enables the development of standard cells alongside ongoing fundamental device research. Thereby, it potentially shortens the development cycle and time to market of a new technology. We develop a new discrete charge-transport model for electrical networks and a new flexible model of polarity-reconfigurable transistors as our formal basis. These models make circuit designs accessible to an analysis using probabilistic model checking and power our experiments. Besides worst-case analysis, we leverage measures hardly accessible to simulation such as average delay and average energy consumption per switching operation. We complement this with an automated design-space exploration that yields all reasonable implementations of a switching function built with reconfigurable transistors. After demonstrating the accuracy of our approach by comparison with finite element method analysis results, we undergo a comprehensive design-space exploration and analysis of the 3-minority function. The quantitative results are ranked with respect to various performance metrics, and we analyze the most promising circuit implementations in detail to derive a design guide that yields the best implementation for given statistics of the input patterns.