A Class of Examples Demonstrating That “P ≠ NP” in the “P Vs NP” Problem

EasyChair Preprint 3198

Abstract

The CMI Millennium “P vs NP Problem” can be resolved e.g. if one shows at least one counterexample to the "P = NP" conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis that "P = NP" for any conditions satisfying the formulation of the problem. Thus, the solution "P is different from NP" of the problem in general 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 exhaustively is formulated.

Keyphrases: Kochen-Specker theorem, P vs NP, Turing machine, computation time, quantum computer, quantum computer as a Turing machine generalization

@booklet{EasyChair:3198,
  author    = {Vasil Penchev},
  title     = {A Class of Examples Demonstrating That “P ≠ NP” in the “P Vs NP” Problem},
  howpublished = {EasyChair Preprint 3198},
  year      = {EasyChair, 2020}}