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.

References

While it is known that P ⊆ NP, whether this inclusion is strict is one of the most important open problems in theoretical computer science.

— On the Complexity of the Secret Protection Problem for Discrete-Event Systems (2509.14372 - Masopust et al., 17 Sep 2025) in Section 2 (Preliminaries), Subsection "Complexity theory"