Liyu Zhang, Mahmoud Quweider, Fitra Khan, Hansheng Lei
{"title":"Splitting NP-complete sets infinitely","authors":"Liyu Zhang, Mahmoud Quweider, Fitra Khan, Hansheng Lei","doi":"10.1016/j.ipl.2024.106472","DOIUrl":null,"url":null,"abstract":"<div><p>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 <em>L</em> can be split into two NP-complete languages <span><math><mi>L</mi><mo>∩</mo><mi>S</mi></math></span> and <span><math><mi>L</mi><mo>∩</mo><mover><mrow><mi>S</mi></mrow><mo>‾</mo></mover></math></span>, where <em>S</em> is a language in P. It follows that every NP-complete language can be partitioned into an arbitrary <em>finite</em> number of NP-complete languages. We strengthen and generalize this result by showing that every NP-complete language can be partitioned into <em>infinitely</em> many NP-complete languages. Furthermore those NP-complete languages resulting from such partitioning can be <em>effectively presented</em>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106472"},"PeriodicalIF":0.7000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Processing Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020019024000024","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
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 and , 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.
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.
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