Journal of Mathematical Sciences

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

Diophantine Hierarchy

  • A. A. Knop

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.


Positive Integer Complexity Class Polynomial Hierarchy 
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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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