无限分割 NP-完全集合

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-01-22 DOI:10.1016/j.ipl.2024.106472

Liyu Zhang, Mahmoud Quweider, Fitra Khan, Hansheng Lei

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引用次数: 0

摘要

Glaßer 等人（SIAMJCOMP 2009 和 TCS 2009）证明了 NP-完全语言在多-一还原时是多项式时间有丝分裂的，这意味着每种 NP-完全语言 L 都可以分割成两种 NP-完全语言 L∩S 和 L∩S‾，其中 S 是 P 中的一种语言。我们通过证明每一种 NP-完全语言都可以被划分为无限多的 NP-完全语言来加强和推广这一结果。此外，这种分割所产生的 NP-完全语言可以有效地呈现出来。

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Splitting NP-complete sets infinitely

Glaßer et al. (SIAMJCOMP 2009 and TCS 2009) proved that NP-complete languages are polynomial-time mitotic for the many-one reduction, meaning that each NP-complete language L can be split into two NP-complete languages $L \cap S$ and $L \cap \overline{S}$ , where S is a language in P. It follows that every NP-complete language can be partitioned into an arbitrary finite number of NP-complete languages. We strengthen and generalize this result by showing that every NP-complete language can be partitioned into infinitely many NP-complete languages. Furthermore those NP-complete languages resulting from such partitioning can be effectively presented.

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.