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Journal of Mathematical Sciences

, Volume 188, Issue 1, pp 59–69 | Cite as

Diophantine Hierarchy

  • A. A. Knop
Article
  • 70 Downloads

In 1975, Adelman and Manders defined the class D of “nondeterministic Diophantine” languages. A language L is in D if and only if there are polynomials p and q such that xL if and only if there exist y 1, …, y n < 2 q(|x|) such that p(x, y 1,…, y n ) = 0 (in this formula, bit strings are treated as positive integers). While, clearly, D is a subset of NP, it is unknown whether these classes coincide.

The well-known polynomial hierarchy PH consists of complexity classes constructed from NP. We consider a hierarchy constructed in a similar way from D. We prove that D lies at the second level of the polynomial hierarchy, and hence all classes of the two hierarchies are successively contained in one another. Bibliography: 6 titles.

Keywords

Positive Integer Complexity Class Polynomial Hierarchy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    L. M. Adleman and K. L. Manders, “Computational complexity of decision procedures for polynomials (extended abstract),” in: IEEE Symposium on Foundations of Computer Science (1975), pp. 169–177.Google Scholar
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    L. M. Adleman and K. L. Manders, “Diophantine complexity,” in: IEEE Symposium on Foundations of Computer Science (1976), pp. 81–88.Google Scholar
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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