On the Relationship between Classes P and NP
- 1 Dahl East-Ukrainian National University, Ukraine
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”.
DOI: https://doi.org/10.3844/jcssp.2012.1036.1040
Copyright: © 2012 Anatoly D. Plotnikov. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Class P
- class NP
- class UF
- set-theoretic model
- problem without foresight
- problem that exponential in nature