Splitting NP-complete sets infinitely

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

引用次数: 0

Abstract

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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无限分割 NP-完全集合

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。

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

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

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