On Computing Minimum Size Prime Implicants

In this paper we describe a new model and algorithm for computing minimum-size prime implicants of Boolean functions. The computation of minimum-size prime implicants has several applications in different areas, including Electronic Design Automation (EDA), Non-Monotonic Reasoning, Logical Inference, among others. For EDA, one significant and immediate application is the computation of minimum-size test patterns in Automatic Test Pattern Generation (ATPG). The proposed approach is based on creating an integer linear program (ILP) formulation for computing the minimum-size prime implicant. In addition, we introduce a new algorithm for solving ILPs, which is built on top of an algorithm for propositional satisfiability (SAT). Experimental results, obtained on several benchmark examples, indicate that our approach is significantly more efficient than existing algorithms.