SAT-Based Generation of Optimum Function Implementations with XOR Gates

This paper presents a method for generating optimum multi-level implementations of Boolean functions. It is based on Satisfiability (SAT) problem solving, while different SAT techniques are employed to reach different targets. The method is able to generate one, or enumerate all optimum implementations, while any technology constraints can be applied. Results for 4 input functions implemented by XOR AND-Inverter-Graphs (XAIGs) with different XOR nodes costs are presented. Scalability and feasibility of the method is presented. Finally, an experimental evaluation of XAIG based rewriting algorithm with optimum replacement circuits is presented and compared with the previous solution.