State Complexity of Boolean Operations on Graph-Walking Automata

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

International Journal of Foundations of Computer Science Pub Date : 2024-07-12 DOI:10.1142/s0129054124420012

O. Martynova, Alexander Okhotin

引用次数: 0

Abstract

Finite automata that traverse graphs by moving along their edges are known as graph-walking automata (GWA). This paper investigates the state complexity of Boolean operations for this model. It is proved that the union of GWA with [Formula: see text] and [Formula: see text] states, with [Formula: see text], operating on graphs with [Formula: see text] labels of edge end-points, is representable by a GWA with [Formula: see text] states, and at least [Formula: see text] states are necessary in the worst case. For the intersection, the upper bound is [Formula: see text] and the lower bound is [Formula: see text]. The upper bound for the complementation is [Formula: see text], and the lower bound is [Formula: see text].

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图行走自动机布尔运算的状态复杂性

通过沿图边移动来遍历图的有限自动机被称为图行走自动机（GWA）。本文研究了该模型布尔运算的状态复杂性。结果证明，具有[公式：见正文]和[公式：见正文]状态的 GWA 的联合，在具有[公式：见正文]边端点标签的图上操作时，可以用具有[公式：见正文]状态的 GWA 表示，而且在最坏情况下至少需要[公式：见正文]个状态。对于交集，上界为[公式：见正文]，下界为[公式：见正文]。补码的上界是[公式：见正文]，下界是[公式：见正文]。

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

International Journal of Foundations of Computer Science 工程技术-计算机：理论方法

CiteScore

1.60

自引率

12.50%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing