An Efficient NPN Boolean Matching Algorithm Based on Structural Signature and Shannon Expansion

TL;DR

This paper introduces a novel NPN Boolean matching algorithm utilizing a structural signature and Shannon expansion, significantly improving speed and efficiency in matching Boolean functions under various transformations.

Contribution

The paper proposes a new structural signature-based algorithm for NPN Boolean matching, reducing search space and increasing speed compared to existing methods.

Findings

Two times faster on equivalent circuit matching

At least one hundred times faster on non-equivalent circuits

Highly effective in solving NPN Boolean matching problem

Abstract

An efficient pairwise Boolean matching algorithm to solve the problem of matching single-output specified Boolean functions under input negation and/or input permutation and/or output negation (NPN) is proposed in this paper. We present the Structural Signature (SS) vector, which is composed of a 1st signature value, two symmetry marks, and a group mark. As a necessary condition for NPN Boolean matching, the structural signature is more effective than is the traditional signature. Two Boolean functions, f and g, may be equivalent when they have the same SS vector. The symmetry mark can distinguish symmetric variables and asymmetric variables and search multiple variable mappings in a single variable-mapping search operation, which reduces the search space significantly. Updating the SS vector using Shannon decomposition provides benefits in distinguishing unidentified variables, and the group mark and the phase collision check discover incorrect variable mappings quickly, which also speeds up the NPN Boolean matching process. Using the algorithm proposed in this paper, we tested both equivalent and non-equivalent matching peeds on the MCNC benchmark circuit sets and the random circuit sets. In the experiment, our algorithm is two times faster than competitors when testing equivalent circuits and averages at least one hundred times faster when testing non-equivalent circuits. The experimental results show that our approach is highly effective in solving the NPN Boolean matching problem.