  Can the computational complexity theory of computer science and mathematics
say something new about unresolved problems in quantum physics? Particularly,
can the P versus NP question in the computational complexity theory be a factor
in the elucidation of the emergency of classicality in quantum mechanics? The
paper compares two different ways of deriving classicality from the quantum
formalism resulted from two differing hypotheses regarding the P versus NP
question -- the approach of the quantum decoherence theory implying that P = NP
and the computational complexity approach which assumes that P is not equal to
NP.
