Boolean-aware Boolean Circuit Classification: A Comprehensive Study on Graph Neural Network

TL;DR

This paper defines the proposed matching-equivalent class based on its ``Boolean-aware'' property and presents a commonly study framework based on graph neural network~(GNN) to analyze the key factors that can affect the Boolean-aware Boolean circuit classification.

Abstract

Boolean circuit is a computational graph that consists of the dynamic directed graph structure and static functionality. The commonly used logic optimization and Boolean matching-based transformation can change the behavior of the Boolean circuit for its graph structure and functionality in logic synthesis. The graph structure-based Boolean circuit classification can be grouped into the graph classification task, however, the functionality-based Boolean circuit classification remains an open problem for further research. In this paper, we first define the proposed matching-equivalent class based on its ``Boolean-aware'' property. The Boolean circuits in the proposed class can be transformed into each other. Then, we present a commonly study framework based on graph neural network~(GNN) to analyze the key factors that can affect the Boolean-aware Boolean circuit classification. The empirical experiment results verify the proposed analysis, and it also shows the direction and opportunity to improve the proposed problem. The code and dataset will be released after acceptance.

Figures (14)

• Figure 1: The illustration of the Boolean transformations of logic optimization and Boolean matching. The previous logic equivalent class generated by logic optimization can be transformed into the "other logic equivalent class" by Boolean matching operations. All these transformations bring about the proposed matching equivalent class.
• Figure 2: The domain relation of the logic equivalency and Boolean matching equivalency.
• Figure 3: The visualization of the full adder under the Boolean transformations. Logic optimization: (a)$\leftrightarrow$(b); Permutation: (a)$\leftrightarrow$(c), and (b)$\leftrightarrow$(d); Negation: (a)$\leftrightarrow$(e), and (b)$\leftrightarrow$(f); Negation$\oplus$Permutation: (c)$\leftrightarrow$(e), and (d)$\leftrightarrow$(f).
• Figure 4: Two NPN-equivalent functions $f$ and $g$.
• Figure 5: The proposed Boolean Circuit Classification Framework.

Theorems & Definitions (12)

• Definition 1: logic/Boolean equivalent
• Definition 2: permutation
• Definition 3: negation
• Definition 4: Boolean matching
• Definition 5: identity
• Remark 1
• Definition 6: logic equivalent class
• Theorem 1
• Proof 1: Proof of \ref{['thm:local_replacement']}
• Definition 7: Matching Equivalent Class