The Complexity of the First-Order Theory of Ground Tree Rewrite Graphs

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Logical Methods in Computer Science Pub Date : 2011-07-05 DOI:10.2168/LMCS-10(1:7)2014

Stefan Goller, Markus Lohrey

引用次数: 2

Abstract

We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.

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地树重写图一阶理论的复杂性

证明了地树重写图的一致一阶理论的复杂度为ATIME(2^{2^{poly(n)}}，O(n))。提供了一个匹配的下界，我们证明了存在一些固定的地面树重写图，其一阶理论对于ATIME(2^{2^{poly(n)}}，poly(n))对于对数空间约简是困难的。最后，我们证明了在正则树语言形式下存在一个固定的地面树重写图和一个一元谓词，使得结果结构具有非初等一阶理论。

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

Logical Methods in Computer Science 工程技术-计算机：理论方法

CiteScore

1.80

自引率

0.00%

发文量

105

审稿时长

6-12 weeks

期刊介绍： Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Topics of Logical Methods in Computer Science: Algebraic methods Automata and logic Automated deduction Categorical models and logic Coalgebraic methods Computability and Logic Computer-aided verification Concurrency theory Constraint programming Cyber-physical systems Database theory Defeasible reasoning Domain theory Emerging topics: Computational systems in biology Emerging topics: Quantum computation and logic Finite model theory Formalized mathematics Functional programming and lambda calculus Inductive logic and learning Interactive proof checking Logic and algorithms Logic and complexity Logic and games Logic and probability Logic for knowledge representation Logic programming Logics of programs Modal and temporal logics Program analysis and type checking Program development and specification Proof complexity Real time and hybrid systems Reasoning about actions and planning Satisfiability Security Semantics of programming languages Term rewriting and equational logic Type theory and constructive mathematics.