[论文解读] Uniform Reduction to SAT

Predrag Janičić|arXiv (Cornell University)|Dec 6, 2010

Model-Driven Software Engineering Techniques被引用 4

一句话总结

本文提出URSA，一种统一的规范语言，结合了命令式与声明式编程范式，可精确地将一大类问题规约为SAT。该系统能够高效求解NP完全问题与有限域约束问题，通过开源实现展示了其与最先进建模系统相当的竞争力。

ABSTRACT

There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system for uniform solving of a wide class of problems by reducing them to SAT. The system uses a new specification language URSA that combines imperative and declarative programming paradigms. The reduction to SAT is defined precisely by the semantics of the specification language. The domain of the approach is wide (e.g., many NP-complete problems can be simply specified and then solved by the system) and there are problems easily solvable by the proposed system, while they can be hardly solved by using other programming languages or constraint programming systems. So, the system can be seen not only as a tool for solving problems by reducing them to SAT, but also as a general-purpose constraint solving system (for finite domains). In this paper, we also describe an open-source implementation of the described approach. The performed experiments suggest that the system is competitive to state-of-the-art related modelling systems.

研究动机与目标

• 为解决缺乏统一、通用的将多样化问题规约为SAT的方法的问题。
• 设计一种规范语言，使用户能够在无需定制工具的情况下，实现精确、语义驱动的SAT编码。
• 基于SAT规约为核心引擎，构建一个用于有限域的通用约束求解器。
• 评估该系统在实际问题求解中与现有建模系统的竞争力。

提出的方法

• 设计URSA，一种领域特定语言，整合命令式与声明式编程以用于问题规范。
• 定义URSA的语义，使其能直接将问题规范映射为用于SAT求解的CNF公式。
• 实现一个开源编译器，将URSA程序转换为标准DIMACS CNF格式。
• 使用现成的SAT求解器作为生成公式的底层求解引擎。
• 支持广泛的问题类型，包括NP完全问题与有限域约束问题。
• 通过高层规范抽象掉底层SAT编码细节，实现统一的问题求解。

实验结果

研究问题

• RQ1 统一的编程语言模型能否以精确语义将多样化问题规约为SAT？
• RQ2 URSA在多大程度上能比传统约束编程系统更自然地求解NP完全问题与有限域问题？
• RQ3 URSA系统在实际应用中的性能与最先进建模系统相比如何？
• RQ4 URSA中命令式与声明式范式的结合，能否在保持效率的同时简化问题规范？

主要发现

• URSA支持对一大类问题（包括许多NP完全问题）进行统一、高层级的规范表达。
• 该系统能够高效求解在传统约束编程语言或通用编程语言中难以表达或求解的问题。
• 开源实现展示了其与最先进建模系统相当的性能表现。
• URSA的精确语义确保了SAT编码的正确性与无歧义性，无需人工干预。
• 通过利用SAT求解，该方法有效充当了通用的有限域约束求解器。
• 实验结果证实了使用统一语言将多样化问题规约为SAT的可行性与高效性。