Journal of
Scientific Research and Studies Vol. 5(2), pp. 3133,
February, 2018
ISSN 23758791
Copyright © 2018
Author(s) retain the
copyright of this article
http://www.modernrespub.org/jsrs/index.htm

Short Communication

A counterexample
of the statement P = NP
Peter
Kopanov
Faculty of Mathematics, Plovdiv
University, 4000 Plovdiv, Bulgaria.
Email:
pkopanov@yahoo.com
Accepted 01 February, 2018


Abstract 

In this paper,
it
is shown that the classes
of P and NP
do not coincide by constructing a relatively simple example of
unsolvability in polynomial time in a particular wellknown
NPcomplete problem.
For a particular NPcomplete problem, a random process is
constructed that generates a solution with random numbers. Such
a solution cannot be found with a polynomial algorithm, but it
can be verified with one if it is known. In this way, the
impossibility of equality P = NP is shown.
Key words: NPcomplete problem, polynomial algorithm,
independent and identically distributed random variables, random
choice. 

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