Fast Exact NPN Classification with Influence-aided Canonical Form

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.

Enhanced Fast Boolean Matching based on Sensitivity Signatures Pruning

Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for an n-variable Boolean function is $O(2^{n+1}n!)$. Sensitivity is an important characteristic and a measure of the complexity of Boolean functions. It has been used in analysis of the complexity of algorithms in different fields. This measure could be regarded as a signature of Boolean functions and has great potential to help reduce the search space of Boolean matching. In this paper, we introduce Boolean sensitivity into Boolean matching and design several sensitivity-related signatures to enhance fast Boolean matching. First, we propose some new signatures that relate sensitivity to Boolean equivalence. Then, we prove that these signatures are prerequisites for Boolean matching, which we can use to reduce the search space of the matching problem. Besides, we develop a fast sensitivity calculation method to compute and compare these signatures of two Boolean functions. Compared with the traditional cofactor and symmetric detection methods, sensitivity is a series of signatures of another dimension. We also show that sensitivity can be easily integrated into traditional methods and distinguish the mismatched Boolean functions faster. To the best of our knowledge, this is the first work that introduces sensitivity to Boolean matching. The experimental results show that sensitivity-related signatures we proposed in this paper can reduce the search space to a very large extent, and perform up to 3x speedup over the state-of-the-art Boolean matching methods.

BlockGNN: Towards Efficient GNN Acceleration Using Block-Circulant Weight Matrices

In recent years, Graph Neural Networks (GNNs) appear to be state-of-the-art algorithms for analyzing non-euclidean graph data. By applying deep-learning to extract high-level representations from graph structures, GNNs achieve extraordinary accuracy and great generalization ability in various tasks. However, with the ever-increasing graph sizes, more and more complicated GNN layers, and higher feature dimensions, the computational complexity of GNNs grows exponentially. How to inference GNNs in real time has become a challenging problem, especially for some resource-limited edge-computing platforms. To tackle this challenge, we propose BlockGNN, a software-hardware co-design approach to realize efficient GNN acceleration. At the algorithm level, we propose to leverage block-circulant weight matrices to greatly reduce the complexity of various GNN models. At the hardware design level, we propose a pipelined CirCore architecture, which supports efficient block-circulant matrices computation. Basing on CirCore, we present a novel BlockGNN accelerator to compute various GNNs with low latency. Moreover, to determine the optimal configurations for diverse deployed tasks, we also introduce a performance and resource model that helps choose the optimal hardware parameters automatically. Comprehensive experiments on the ZC706 FPGA platform demonstrate that on various GNN tasks, BlockGNN achieves up to $8.3\times$ speedup compared to the baseline HyGCN architecture and $111.9\times$ energy reduction compared to the Intel Xeon CPU platform.