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Journal of Scientific Research and  Studies

Journal of Scientific Research and Studies Vol. 5(2), pp. 31-33, February, 2018

ISSN 2375-8791

Copyright 2018

Author(s) retain the copyright of this article


Short Communication

A counterexample of the statement P = NP


Peter  Kopanov

Faculty of Mathematics, Plovdiv University, 4000 Plovdiv, Bulgaria.

Accepted 01 February, 2018




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 well-known NP-complete problem. For a particular NP-complete 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: NP-complete problem, polynomial algorithm, independent and identically distributed random variables, random choice.

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Vol. 5 Issue 2

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