Fast heuristic and exact algorithms for two-level hazard-free logic minimization

None of the available minimizers for 2-level hazard-free logic minimization can synthesize very large circuits. This limitation has forced researchers to resort to manual and automated circuit partitioning techniques. This paper introduces two new 2-level logic minimizers: Espresso-HF, a heuristic method which is loosely based on Espresso-II, and Impymin, an exact method based on implicit data structures. Both minimizers can solve all currently available examples, which range up to 32 inputs and 33 outputs. These include examples that have never been solved before. For examples that can be solved by other minimizers our methods are several orders of magnitude faster. As by-products of these algorithms, we also present two additional results. First, we introduce a fast new algorithm to check if a hazard-free covering problem can feasibly be solved. Second, we introduce a novel formulation of the 2-level hazard-free logic minimization problem by capturing hazard-freedom constraints within a synchronous function by adding new variables.