Languages given by finite automata over the unary alphabet

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

Abstract

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.