Fast Exact NPN Classification with Influence-aided Canonical Form

Abstract: NPN classification has many applications in the synthesis and verification of digital circuits. The canonical-form-based method is the most common approach, designing a canonical form as representative for the NPN equivalence class first and then computing the transformation function according to the canonical form. Most works use variable symmetries and several signatures, mainly based on the cofactor, to simplify the canonical form construction and computation. This paper describes a novel canonical form and its computation algorithm by introducing Boolean influence to NPN classification, which is a basic concept in analysis of Boolean functions. We show that influence is input-negation-independent, input-permutation-dependent, and has other structural information than previous signatures for NPN classification. Therefore, it is a significant ingredient in speeding up NPN classification. Experimental results prove that influence plays an important role in reducing the transformation enumeration in computing the canonical form. Compared with the state-of-the-art algorithm implemented in ABC, our influence-aided canonical form for exact NPN classification gains up to 5.5x speedup.