有限自动机在一元字母表上给出的语言

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2025-02-05 DOI:10.1016/j.jcss.2025.103634

Wojciech Czerwiński , Maciej Dębski , Tomasz Gogasz , Gordon Hoi , Sanjay Jain , Michał Skrzypczak , Frank Stephan , Christopher Tan

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引用次数: 0

摘要

本文研究了有限自动机在字母表为一元时的运算复杂性及其决策问题的复杂性。设n表示所考虑的输入自动机的状态数。得到了以下主要结果：(1)在2O（(nlog ln n)1/3）时间内，可以确定NFAs是否相等和是否包含。以前的上界2O(（nlog (n)1/2）是由Chrobak（1986）提出的。(2)可以用最多拟多项式的状态数来确定另一个UFA的补或两个UFA的并的UFA（无二义有限自动机）。然而，对于两个n态UFA的连接，最坏的情况是UFA具有2Θ(（nlog2 (n)1/3）状态。(3)当UFA或NFA给出的无限ω词是给定正则ω语言的成员时，得到了结果。

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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Languages given by finite automata over the unary alphabet

This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let n denote the number of states of the input automata considered. The following main results are obtained:

(1) Equality and inclusion of NFAs can be decided within time

2^{O ({(n \log n)}^{1 / 3})}

. The previous upper bound

2^{O ({(n \log n)}^{1 / 2})}

was by Chrobak (1986).

(2) One can determine a UFA (unambiguous finite automata) for complement of another UFA or union of two UFAs using at most quasipolynomial number of states. However, for concatenation of two n-state UFAs, the worst case is a UFA having

2^{Θ ({(n \log^{2} n)}^{1 / 3})}

states.

(3) Results when an infinite ω-word given by a UFA or an NFA is a member of a given regular ω-language are obtained.

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.