Working with ARMs

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS
G. Gottlob, R. Pichler
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引用次数: 3

Abstract

An atomic representation of a Herbrand model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM represents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of computer science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs.The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMs, and evaluating clauses over ARMs. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In this paper, we prove that all mentioned problems are coNP-complete.
与arm合作
Herbrand模型(ARM)的原子表示是给定Herbrand宇宙上的有限原子集(不一定是基本的)。每一个ARM代表了一个可能无限的Herbrand诠释。这个概念已经独立出现在计算机科学的不同分支中,作为有限Herbrand解释概念的自然和有用的推广。证明了有限Herbrand模型(或解释)上的几个递归可决问题在arm上仍然是可决的。在使用ARMs时,下列问题是必不可少的:确定两个ARMs的等价性,确定ARMs之间的包容,以及评估ARMs上的条款。这些问题被证明是可决定的,但它们的计算复杂性至今仍是模糊的。先前发表的决策算法需要指数空间。在本文中,我们证明了上述所有问题都是conp完备的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Quantum Information & Computation
Quantum Information & Computation 物理-计算机:理论方法
CiteScore
1.70
自引率
0.00%
发文量
42
审稿时长
3.3 months
期刊介绍: Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.
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