An Equivalence between Polynomial Constructivity of Markov’s Principle and the Equality P=NP

  • V. Yu. Sazonov

Keywords

Berman tlCl 

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References

  1. Berman P., 1983, Review on [Sazonov, 1980], M.R., 83j: 68055.Google Scholar
  2. Riss S.R., 1986, “Bounded Arithmetic”, Bibliopolis, Napoli, 221 pp.Google Scholar
  3. Dragalin A.G., 1979, “Mathematical Intuitionism Introduction to proof theory”, Nauka, Moscow, 256pp. (In Russian)MATHGoogle Scholar
  4. Girard J.-Y., 1987, “Proof Theory and Logical Complexity”, Vol. 1, Bibliopolis, Napoli, 503 pp.MATHGoogle Scholar
  5. Sazonov V.Yu., 1980, A logical approach to the problem “P=NP?”, in: Lecture Notes in Computer Science, N88, Springer, New York, P.562–575. (An important correction to this paper is given in [Sazonov, 1981, P.490.])Google Scholar
  6. Sazonov V.Yu., 1981, On existence of complete predicate calculus in metamathematics without exponentiation, in:Lecture Notes in Computer Science, N118, Springer, New York, P. 483–490.Google Scholar
  7. Sazonov V.Yu., 1987, An equivalence between polynomial constructivity of Markov“s principle and the equality P=NP, in: ”19th All-Union Algebraic Conference, Proceedings“, part 2, L”vov, P.250–251. (In Russian) (A paper with the same title will be published in the Proceedings of Institute of Mathematics, Siberian Branch of USSR Akademy of Sciences, Novosibirsk, 1989, about 80 of typescript pages.)Google Scholar
  8. Takeuti G., 1975, “Proof theory”, North-Holland, Amsterdam.Google Scholar
  9. Troelstra A., 1977, Aspects of constructive mathematics, in: “Handbook of Mathematical Logic”, J.Barwise, ed., North-Holland, Amsterdam.Google Scholar
  10. Yessenin-Vol’pin A.S., 1959, An analysis of potential feasibility, in: “Logic investigations”, Moscow, P.218–262. (In Russian)Google Scholar
  11. Zvonkin A.K. and Levin L.A., 1970, Complexity of finite objects and foundation of information and randomness notions through algorithms theory, Uspechi Mat. Nauk Vo1.25, N6, P. 85–127. (In Russian)MathSciNetGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • V. Yu. Sazonov
    • 1
  1. 1.Institute of Program Systems of USSR Akademy of SciencesPereslavl’-ZalesskyUSSR

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