A class of examples demonstrating that P is different from NP in the "P vs NP" problem

TL;DR

This paper presents a class of counterexamples involving quantum superpositions and the Kochen-Specker theorem to demonstrate that P is not equal to NP, providing a proof for the separation of these complexity classes.

Contribution

It introduces a novel class of counterexamples based on quantum superpositions and the Kochen-Specker theorem, offering a new approach to resolve the P vs NP problem.

Findings

Counterexamples involve quantum superpositions of finite quantum states

Fundamentally random choices belong to NP but not to P

The set complement of P in NP can be characterized by quantum-like choices

Abstract

The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows at least one counterexample to the conjecture "P is equal to NP". A certain class of problems being such counterexamples is formulated. This implies the rejection of the hypothesis "P is equal to NP" for any conditions satisfying the formulation of the problem. Thus, the solution "P is different from NP" of the problem is proved. The class of counterexamples can be interpreted as any quantum superposition of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to NP, but not to P. The conjecture that the set complement of P to NP can be described by that kind of choice is formulated exhaustively.