Research Article Open Access

On the Relationship between Classes P and NP

Anatoly D. Plotnikov1
  • 1 Dahl East-Ukrainian National University, Ukraine
Journal of Computer Science
Volume 8 No. 7, 2012, 1036-1040

DOI: https://doi.org/10.3844/jcssp.2012.1036.1040

Published On: 16 May 2012

How to Cite: Plotnikov, A. D. (2012). On the Relationship between Classes P and NP. Journal of Computer Science, 8(7), 1036-1040. https://doi.org/10.3844/jcssp.2012.1036.1040

Abstract

Problem statement: In this study we discuss the relationship between the known classes P and NP. We show that the difficulties in solving problem “P versus NP” have methodological in nature. An algorithm for solving any problem is sensitive to even small changes in its formulation. Conclusion/Recommendations: As we will show in the study, these difficulties are exactly in the formulation of some problems of the class NP. We construct a class UF that contains P and that simultaneously is strictly contained in NP. Therefore, a new problem arises “P versus UF”.

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Keywords

  • Class P
  • class NP
  • class UF
  • set-theoretic model
  • problem without foresight
  • problem that exponential in nature