Informatics and Engineering Systems Faculty Publications and Presentations

Splitting NP-complete sets infinitely

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.

Publication Title

Information Processing Letters

DOI

10.1016/j.ipl.2024.106472

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