Splitting NP-complete sets infinitely

Authors

• Liyu Zhang, The University of Texas Rio Grande ValleyFollow
• Mahmoud K. Quweider, The University of Texas Rio Grande Valley
• Fitratullah Khan, The University of Texas Rio Grande Valley
• Hangsheng Lei, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

8-2024

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 ∩ S and L ∩ ¯¯¯ 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.

Recommended Citation

Zhang, Liyu, Mahmoud Quweider, Fitra Khan, and Hansheng Lei. "Splitting NP-complete sets infinitely." Information Processing Letters 186 (2024): 106472. https://doi.org/10.1016/j.ipl.2024.106472

Publication Title

Information Processing Letters

DOI

10.1016/j.ipl.2024.106472