BoolGebra: Attributed Graph-learning for Boolean Algebraic Manipulation

TL;DR

The paper tackles the challenge of scalable Boolean algebraic manipulation in logic synthesis where traditional DAG-aware optimizations risk missing opportunities and suffer from combinatorial growth. It introduces BoolGebra, a Graph Neural Network-based predictor that ingests AIG structure with function-aware embeddings to forecast per-node optimization impact, guiding a single AIG traversal that orchestrates rw, rs, and rf. The approach combines priority-guided random sampling, static/dynamic node features, a GraphSAGE encoder, and a dense predictor to shrink the search space and locate high-quality optimizations, integrated with the ABC synthesis tool for end-to-end evaluation. Empirical results show design-specific and cross-design generalization with improvements over SOTA stand-alone optimizations by up to 5.5%, highlighting BoolGebra's potential to scale Boolean manipulation in large, real-world designs.

Abstract

Boolean algebraic manipulation is at the core of logic synthesis in Electronic Design Automation (EDA) design flow. Existing methods struggle to fully exploit optimization opportunities, and often suffer from an explosive search space and limited scalability efficiency. This work presents BoolGebra, a novel attributed graph-learning approach for Boolean algebraic manipulation that aims to improve fundamental logic synthesis. BoolGebra incorporates Graph Neural Networks (GNNs) and takes initial feature embeddings from both structural and functional information as inputs. A fully connected neural network is employed as the predictor for direct optimization result predictions, significantly reducing the search space and efficiently locating the optimization space. The experiments involve training the BoolGebra model w.r.t design-specific and cross-design inferences using the trained model, where BoolGebra demonstrates generalizability for cross-design inference and its potential to scale from small, simple training datasets to large, complex inference datasets. Finally, BoolGebra is integrated with existing synthesis tool ABC to perform end-to-end logic minimization evaluation w.r.t SOTA baselines.

Figures (6)

• Figure 1: The optimized graph produced by stand-alone optimization operations and orchestration operation: (a) original AIG, graph size is 21; (b) optimized AIG with stand-alone rw, graph size is 19; (b) optimized AIG with stand-alone rf, graph size is 19; (c) optimized AIG with stand-alone rs, graph size is 20; (d) optimized AIG with proposed Algorithm \ref{['alg:orch']}, graph size is 16.
• Figure 2: The optimization quality distribution with 6000 samples of purely random sampling and priority guided sampling.
• Figure 3: The design flow of BoolGebra including the feature embeddings with static and dynamic sampling embeddings ((a) -- (f)), and the model construction ((g)).
• Figure 4: Design-specific testing loss w.r.t training epochs.
• Figure 5: Design-specific inference evaluation for predicting AIG minimization performance for given manipulation decisions. Each sub-figure corresponds to an individual design, where the inference input are unseen randomly sampled decisions, where $x$-axis represents the normalized prediction and $y$-axis represents the normalized ground truth. Note that value "0" refers to the best quality-of-results and "1" refers to the worst.