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Transactions of Tianjin University

, Volume 17, Issue 6, pp 446–449 | Cite as

A non-canonical example to support P is not equal to NP

  • Zhengling Yang (杨正瓴)Email author
Article
  • 74 Downloads

Abstract

The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor’s theorem, it is shown that an NTM is not equipotent to a DTM. This means that “generating the power set P(A) of a set A” is a non-canonical example to support that P is not equal to NP.

Keywords

P versus NP computational complexity theory Cantor’s theorem power set continuum hypothesis 

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References

  1. [1]
    Cook S. The P versus NP Problem. Official Problem Description[EB/OL]. http://www.claymath.org/millennium/P_vs_NP/pvsnp.pdf, 2000.
  2. [2]
    Encyclopaedia of China: Electronics and Computer[M]. Encyclopaedia of China Publishing House, Beijing, 1986 (in Chinese).Google Scholar
  3. [3]
    The Clay Mathematics Institute. P vs NP Problem [EB/OL]., http://www.,claymath.,org/millennium/P_vs_NP/, 2000.
  4. [4]
    Smale S. Mathematical problems for the next century[J]. Mathematical Intelligencer, 1998, 20(2): 7–15.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    Seife C. What are the limits of conventional computing?[J]. Science, 2005, 309(5731): 96.CrossRefGoogle Scholar
  6. [6]
    Gasarch W I. The P=?NP poll[J]. SIGACT News, 2002, 33(2): 34–47.CrossRefGoogle Scholar
  7. [7]
    Allender E. A status report on the P versus NP question[J]. Advances in Computers, 2009, 77: 117–147.CrossRefGoogle Scholar
  8. [8]
    Fortnow L. The status of the P versus NP problem[J]. Communications of the ACM, 2009, 52(9): 78–86.CrossRefGoogle Scholar
  9. [9]
    Cook S. The importance of the P versus NP question[J]. Journal of the ACM, 2003, 50(1): 27–29.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Gassner C. Oracles and relativizations of the P =? NP question for several structures[J]. Journal of Universal Computer Science, 2009, 15(6): 1186–1205.zbMATHMathSciNetGoogle Scholar
  11. [11]
    Manea F, Margenstern M, Mitrana V et al. A new characterization of NP, P, and PSPACE with accepting hybrid networks of evolutionary processors[J]. Theory of Computing Systems, 2010, 46(2): 174–192.CrossRefzbMATHMathSciNetGoogle Scholar
  12. [12]
    Mukund M. NP-Completeness not the same as separating P from NP[J]. Communications of the ACM, 2009, 52(4): 9.CrossRefGoogle Scholar
  13. [13]
    Kuratowski K, Mostowski A. Set Theory[M]. North-Holland Publishing Company, Amsterdam, 1976.Google Scholar
  14. [14]
    Hazewinkel M. Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet “Mathematical Encyclopaedia”[M]. Kluwer Academic Publishers, Dordrecht, 2001.Google Scholar
  15. [15]
    Hopcroft J E, Motwani R M, Ullman J D. Introduction to Automata Theory, Languages and Computation[M]. 3 edition. Addison Wesley, New Jersey, 2006.Google Scholar
  16. [16]
    Garey M R, Johnson D S. Computers and Intractability: A Guide to the Theory of NP-Completeness[M]. New York: W. H. Freeman, 1979.Google Scholar
  17. [17]
    Nondeterministic, Turing, Machine[EB/OL]., http://mathworld.wolfram.com/NondeterministicTuringMachine.html, 2011.
  18. [18]
    Chaitin G J. Information-theoretic computational complexity [J]. IEEE Transactions on Information Theory, 1974, 20(1): 10–15.CrossRefzbMATHMathSciNetGoogle Scholar
  19. [19]
    Encyclopaedia of China: Mathematics[M]. Encyclopaedia of China Publishing House, Beijing, 1988 (in Chinese).Google Scholar

Copyright information

© Tianjin University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Electrical Engineering and AutomationTianjin UniversityTianjinChina
  2. 2.Tianjin Key Laboratory of Process Measurement and ControlTianjinChina

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