Optimizing SAT Solving Efficiency through EDA-Driven Preprocessing

Core Concepts

An innovative EDA-driven preprocessing framework that seamlessly integrates into the SAT solving pipeline, efficiently reformulating SAT problems by converting standard CNF formulas into circuits and optimizing them for easier solving.

Abstract

The paper introduces an EDA-driven preprocessing framework for improving the efficiency of SAT solving. The key aspects of the framework are:

Conversion of CNF formulas into circuit format (And-Inverter Graphs, AIGs) to leverage advanced circuit optimization techniques.
Exploration of optimal logic synthesis strategies using a reinforcement learning (RL) agent, which aims to directly minimize the solving complexity.
Integration of a cost-customized LUT mapping approach that prioritizes reducing the branching complexity during SAT solving, rather than solely focusing on problem size reduction.
Transformation of the optimized LUT netlist back into a simplified CNF format for compatibility with modern SAT solvers.

The framework demonstrates substantial performance improvements, achieving a 52.42% reduction in average solving time for SAT competition benchmarks and a remarkable 96.14% runtime reduction for a set of logic equivalence checking problems.

Stats

The number of gates in the initial circuit instances ranges from 60 to 24,178, with an average of 4,299.06 gates.
The number of primary inputs ranges from 6 to 102, with an average of 43.66.
The circuit depth ranges from 18 to 138, with an average of 66.43.
The number of clauses in the initial CNF instances ranges from 131 to 60,294, with an average of 10,687.28.
The initial solving time without preprocessing ranges from 0.04 to 6.68 seconds, with an average of 2.01 seconds.

Quotes

"Effective formulation of problems into Conjunctive Normal Form (CNF) is critical in modern Boolean Satisfiability (SAT) solving for optimizing solver performance."
"A major challenge within the existing SAT solving framework is the absence of a universally efficient formulation mechanism."
"To address these challenges, we introduce an Electronic Design Automation (EDA)-driven preprocessing framework, a novel integration into the standard SAT solving pipeline."

Key Insights Distilled From

EDA-Driven Preprocessing for SAT Solving

by Zhengyuan Sh... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19446.pdf

Deeper Inquiries

How can the proposed framework be extended to handle a wider range of SAT problem types, including those without inherent circuit structures

The proposed framework can be extended to handle a wider range of SAT problem types, including those without inherent circuit structures, by incorporating more diverse preprocessing techniques. One approach could involve integrating machine learning algorithms to identify patterns and structures in the SAT instances that can guide the preprocessing steps. For SAT problems without natural circuit structures, the framework could utilize graph-based representations or other alternative formats to capture the problem's essence. By adapting the preprocessing techniques to suit different problem types, the framework can enhance its versatility and effectiveness in handling a broader spectrum of SAT instances.

What are the potential limitations or drawbacks of the cost-customized LUT mapping approach, and how could it be further improved

One potential limitation of the cost-customized LUT mapping approach is the complexity of defining an accurate cost metric that effectively captures the solving complexity of the SAT instances. The cost function used in the mapping process may not always perfectly align with the actual solving time reduction, leading to suboptimal results in some cases. To address this limitation, the cost metric could be refined by incorporating additional factors that influence the solving complexity, such as the structure of the circuit, the distribution of gates, or the presence of critical paths. By enhancing the cost function to better reflect the actual solving challenges, the mapping approach can be further improved in optimizing the SAT instances for efficient solving.

Given the significant performance gains on logic equivalence checking problems, how could the insights from this work be applied to other verification tasks, such as model checking or hardware-software co-verification

The insights gained from the significant performance gains on logic equivalence checking problems can be applied to other verification tasks, such as model checking or hardware-software co-verification, by leveraging similar preprocessing strategies tailored to the specific requirements of these tasks. For model checking, the framework can be adapted to transform the model descriptions into optimized formats that facilitate efficient verification. Similarly, for hardware-software co-verification, the preprocessing techniques can be customized to handle the interaction between hardware and software components, streamlining the verification process. By extending the framework's capabilities to these verification tasks, the efficiency and effectiveness of the overall verification process can be significantly enhanced.