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A model-theoretic proof for P ≠ NP over all infinite abelian group

Published online by Cambridge University Press:  12 March 2014

Mihai Prunescu
Mihai Prunescu*
Affiliation:
Institut für Mathematik und Informatik der Universität Greifswald, F.L.Jahn STR. 15A, 17489 Greifswald, Germany Institute of Mathematics of Romanian Academy, PO-Box 1-764, 70700 Bucharest, Romania, E-mail: [email protected]
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Abstract

We give a model-theoretic proof of the fact that for all infinite Abelian groups P ≠ NP in the sense of binary nondeterminism. This result has been announced 1994 by Christine Gaßner.

Keywords

BSS-modelP ≠ NPabelian groupultraproduct
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 1 , March 2002 , pp. 235 - 238
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[A]Asser, Günter, Gaßner, Christine, and Prunescu, Mihai, Für alle unendlichen abelschen Gruppen G ist P(G) ≠ NP(G). (drei Beweise), preprint der Universität Greifswald, January 2000.Google Scholar
[BCSS]Blum, Lenore, Cucker, Felipe, Shub, Michael, and Smale, Steven, Complexity and real computation, Springer-Verlag, New-York, 1998.CrossRefGoogle Scholar
[BSS]Blum, Lenore, Shub, Michael, and Smale, Steven, On a theory of computation and complexity over the real numbers, American Mathematical Society Bulletin, vol. 21 (1989).CrossRefGoogle Scholar
[B]Bourgade, Menard, Separations et transferts dans la hierarchie polynomiale des groupes abeliens infinis, preprint, 2000.3.0.CO;2-S>CrossRefGoogle Scholar
[H]Hemmerling, Armin, On P vs. NP for parameter-free programs over algebraic structures, to appear in Mathematical Logic Quarterly.Google Scholar
[M]Meer, Klaus, Real number models under various sets of operations, Journal of Complexity, vol. 9, 1993.CrossRefGoogle Scholar
[P]Poizat, Bruno, Lespetits cailloux, Aleas, Lyon, 1995.Google Scholar