Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

BDD2Seq: Enabling Scalable Reversible-Circuit Synthesis via Graph-to-Sequence Learning

Mingkai Miao, Jianheng Tang, Guangyu Hu, Hongce Zhang

TL;DR

BDDs provide compact representations of Boolean functions, but optimal variable ordering for ROBDDs is NP-hard and critically affects Quantum Cost in reversible-circuit synthesis. BDD2Seq addresses this by learning a graph-to-sequence mapping: a Graph Neural Network encodes circuit structure (via BLIF2Graph) and a Pointer Network decodes variable orderings, guided by Diverse Beam Search to explore diverse, high-quality permutations. Trained on supervised labels from established BDD heuristics and evaluated with Revkit on multiple benchmarks, it achieves substantial reductions in Quantum Cost (about 1.4x) and faster synthesis (about 3.7x) compared with traditional heuristics, particularly for large circuits. The approach demonstrates that graph-based generative modeling, combined with diversity-aware decoding, can robustly improve BDD-based reversible-circuit synthesis with scalable performance and multiple deployment modes for cost-speed trade-offs.

Abstract

Binary Decision Diagrams (BDDs) are instrumental in many electronic design automation (EDA) tasks thanks to their compact representation of Boolean functions. In BDD-based reversible-circuit synthesis, which is critical for quantum computing, the chosen variable ordering governs the number of BDD nodes and thus the key metrics of resource consumption, such as Quantum Cost. Because finding an optimal variable ordering for BDDs is an NP-complete problem, existing heuristics often degrade as circuit complexity grows. We introduce BDD2Seq, a graph-to-sequence framework that couples a Graph Neural Network encoder with a Pointer-Network decoder and Diverse Beam Search to predict high-quality orderings. By treating the circuit netlist as a graph, BDD2Seq learns structural dependencies that conventional heuristics overlooked, yielding smaller BDDs and faster synthesis. Extensive experiments on three public benchmarks show that BDD2Seq achieves around 1.4 times lower Quantum Cost and 3.7 times faster synthesis than modern heuristic algorithms. To the best of our knowledge, this is the first work to tackle the variable-ordering problem in BDD-based reversible-circuit synthesis with a graph-based generative model and diversity-promoting decoding.

BDD2Seq: Enabling Scalable Reversible-Circuit Synthesis via Graph-to-Sequence Learning

TL;DR

BDDs provide compact representations of Boolean functions, but optimal variable ordering for ROBDDs is NP-hard and critically affects Quantum Cost in reversible-circuit synthesis. BDD2Seq addresses this by learning a graph-to-sequence mapping: a Graph Neural Network encodes circuit structure (via BLIF2Graph) and a Pointer Network decodes variable orderings, guided by Diverse Beam Search to explore diverse, high-quality permutations. Trained on supervised labels from established BDD heuristics and evaluated with Revkit on multiple benchmarks, it achieves substantial reductions in Quantum Cost (about 1.4x) and faster synthesis (about 3.7x) compared with traditional heuristics, particularly for large circuits. The approach demonstrates that graph-based generative modeling, combined with diversity-aware decoding, can robustly improve BDD-based reversible-circuit synthesis with scalable performance and multiple deployment modes for cost-speed trade-offs.

Abstract

Binary Decision Diagrams (BDDs) are instrumental in many electronic design automation (EDA) tasks thanks to their compact representation of Boolean functions. In BDD-based reversible-circuit synthesis, which is critical for quantum computing, the chosen variable ordering governs the number of BDD nodes and thus the key metrics of resource consumption, such as Quantum Cost. Because finding an optimal variable ordering for BDDs is an NP-complete problem, existing heuristics often degrade as circuit complexity grows. We introduce BDD2Seq, a graph-to-sequence framework that couples a Graph Neural Network encoder with a Pointer-Network decoder and Diverse Beam Search to predict high-quality orderings. By treating the circuit netlist as a graph, BDD2Seq learns structural dependencies that conventional heuristics overlooked, yielding smaller BDDs and faster synthesis. Extensive experiments on three public benchmarks show that BDD2Seq achieves around 1.4 times lower Quantum Cost and 3.7 times faster synthesis than modern heuristic algorithms. To the best of our knowledge, this is the first work to tackle the variable-ordering problem in BDD-based reversible-circuit synthesis with a graph-based generative model and diversity-promoting decoding.

Paper Structure

This paper contains 27 sections, 3 equations, 8 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Binary Decision Diagram
  4. Reversible Circuit Synthesis
  5. Graph Learning for EDA Tasks
  6. Pointer Network with Diverse Beam Search
  7. Methodology
  8. Overview of framework
  9. Training Phase.
  10. Inference Phase with Reversible Circuit Synthesis.
  11. Circuit Embedding - BLIF2Graph
  12. Variable Ordering Prediction
  13. Pointer‑Network Decoding Loop.
  14. Diverse Beam Search.
  15. Experiments
  16. ...and 12 more sections

Figures (8)

  • Figure 1: $f=(x_0x_1\lor x_2x_3\lor x_4x_5)$ with different orderings
  • Figure 2: Overall training phase
  • Figure 3: Inference phase with reversible circuit synthesis
  • Figure 4: BLIF2Graph: BLIF to graph with embeddings
  • Figure 5: Pointer Network decoding loop
  • ...and 3 more figures