P vs NP problem

Determine whether the complexity classes P and NP are equal, thereby resolving the P versus NP problem.

Background

The paper surveys exponential lower bounds for monotone circuits computing natural graph properties (e.g., clique and perfect matching) and explains how sunflowers contribute to these bounds. However, extending such exponential lower bounds to general Boolean circuits (which allow negations) would imply P ≠ NP.

Since proving superpolynomial lower bounds for general circuits strong enough to separate P from NP remains elusive, the P vs NP problem is highlighted as a central open question in this context.

References

Proving similar exponential lower bounds for general Boolean circuits (which allow negations) would resolve the $\mathsf{P}$ vs $\mathsf{NP}$ problem, a major open question in computer science.

— The Story of Sunflowers  (2509.14790 - Rao, 18 Sep 2025) in Section 2.2 (Monotone circuit complexity)

Its central open question—whether P equals NP—asks whether every truth that can be verified efficiently can also be constructed.

— From Heisenberg and Schrödinger to the P vs. NP Problem  (2511.07502 - Weinstein, 10 Nov 2025) in Section 1. Introduction

Evidently, ${P} \subseteq {NP}$, and it is a major open question (in fact, one out of the six remaining Millennium Prize Problem ; the Poincaré Conjecture is now proven) whether ${P} = {NP}$.

— Spacetime Quasicrystals and Computational Complexity Theory in the Road Towards Quantum Gravity  (2610.09855 - Mygdalas, 7 Oct 2026) in Chapter 1, Section 1.1, 'The P versus NP Problem and the Physical Extended Church--Turing Thesis'