Parallel Gröbner Basis Rewriting and Memory Optimization for Efficient Multiplier Verification

Hongduo Liu, Peiyu Liao, Junhua Huang, Hui-Ling Zhen, Mingxuan Yuan, Tsung-Yi Ho, Bei Yu

Abstract: Formal verification of integer multipliers is a significant but time-consuming problem. This paper introduces a novel approach that emphasizes the acceleration of symbolic computer algebra (SCA)-based verification systems from the perspective of efficient implementation instead of traditional algorithm enhancement. Our first strategy involves leveraging parallel computing to accelerate the rewriting process of the Gröbner basis. Confronting the issue of frequent memory operations during the Gröbner basis reduction phase, we propose a double buffering scheme coupled with an operator scheduler to minimize memory allocation and deallocation. These unique contributions are integrated into a state-of-the-art verification tool and result in substantial improvements in verification speed, demonstrating more than 15× speedup for a 1024×1024 multiplier.