Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of examples demonstrating that P is different from NP in the "P
  vs NP" problem   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.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph