Symmetry-Based Synthesis for Interpretable Boolean Evaluation

Efficient evaluation of Boolean functions is a fundamental problem in computer science, impacting computational complexity and hardware performance. A natural way to evaluate Boolean functions is using circuits composed of two-input operators. However, synthesizing minimum circuits for functions with more than 6 inputs is typically infeasible. This paper introduces an engine based on Edward's theory of symmetry-based remapping for synthesizing Boolean chains. The proposed engine can synthesize functions with up to 20 inputs within seconds, surpassing state-of-the-art tools that require extensive hyper-parameter tuning to handle similar functions and fail to scale beyond that. Additionally, it enhances the interpretability of Boolean chains, uncovering recursive substructures that facilitate optimality proofs and inform bit-wise manipulation algorithms,