P versus NP strict inclusion

Determine whether the complexity class P is strictly contained in NP, equivalently, establish whether P ≠ NP.

Background

In their preliminaries on computational complexity, the authors review the standard classes P and NP and highlight the long-standing uncertainty regarding their relationship. This is presented as general context for the complexity results developed later in the paper.

The statement emphasizes that although it is known P ⊆ NP, it is an open problem to decide whether this inclusion is strict, i.e., whether P ≠ NP. This foundational question underpins many complexity-theoretic hardness results referenced throughout the paper.