Exact Minimum Factoring of Incompletely Specified Logic Functions via Quantified Boolean Satisfiability

This paper presents an exact method which finds the minimum factored form of an incompletely specified Boolean function. The problem is formulated as a Quantified Boolean Formula (QBF) and is solved by general-purpose QBF solver. We also propose a novel graph structure, called an X-B (eXchanger Binary) tree, which compactly and implicitly enumerates binary trees. Leveraged by this graph structure, the factoring problem is transformed into a QBF. Using three sets of benchmark functions: artificially-created, randomly-generated and ISCAS 85 benchmark functions, we empirically demonstrate the quality of the solutions and the runtime complexity of the proposed method.