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引用次数: 0
摘要
近年来,人们对研究强于解析(Resolution)的证明系统越来越感兴趣,目的是在此基础上建立更高效的 SAT 解算器。在定义这些证明系统时,我们试图在证明系统的能力(反驳公式所需的证明的大小)和寻找证明的难度之间找到平衡。在本文中,我们考虑了循环解析、Sherali-Adams、Nullstellensatz 和加权解析等证明系统,并从理论角度研究了它们的相对能力。我们证明循环解析、Sherali-Adams 和加权解析是多项式等价的证明系统。我们还证明了 Nullstellensatz 多项式等价于加权解析的限制版本。这些等价性也适用于系数/权重以一元形式表示的系统版本。这些系统的实际意义在于,在这些系统的宽度/阶数较小的情况下,它们可以采用高效算法找到证明。
In recent years there has been an increasing interest in studying proof systems stronger than Resolution, with the aim of building more efficient SAT solvers based on them. In defining these proof systems, we try to find a balance between the power of the proof system (the size of the proofs required to refute a formula) and the difficulty of finding the proofs.
In this paper we consider the proof systems circular Resolution, Sherali-Adams, Nullstellensatz and Weighted Resolution and we study their relative power from a theoretical perspective. We prove that circular Resolution, Sherali-Adams and Weighted Resolution are polynomially equivalent proof systems. We also prove that Nullstellensatz is polynomially equivalent to a restricted version of Weighted Resolution. The equivalences carry on also for versions of the systems where the coefficients/weights are expressed in unary.
The practical interest in these systems comes from the fact that they admit efficient algorithms to find proofs in case these have small width/degree.
期刊介绍:
ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.