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Structure with fast elimination of quantifiers

Published online by Cambridge University Press:  12 March 2014

Mihai Prunescu
Mihai Prunescu*
Affiliation:
Abteiling für Mathematische Logik, Universität Freiburg, Ecker STR. 1, D-79103 Freiburg im Breisgau, Germany I. M. A. R. (Institutul de Matematica“Simion Stoilow” al Academiei Romane) Calea Grivitei STR. 21, Ro-010702 Bucharest, Romania. E-mail: michai.prunescu@math.uni-freiburg.de
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Abstract

A structure of finite signature is constructed so that: for all existential formulas and for all tuples of elements of the same length as the tuple one can decide in a quadratic time depending only on the length of the formula, if holds in the structure. In other words, the structure satisfies the relativized model-theoretic version of P=N P in the sense of [4]. This is a model-theoretical approach to results of Hemmerling and Gaßner.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 321 - 328
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

[1]Gaßner, Christine, A structure of finite signature with identity relation and with P = NP—A formal proof, preprint, Universität Greifswald, 2004.Google Scholar
[2]Hemmerling, Armin, P = NP for some structures over the binary words, Journal of Complexity, vol. 21 (2005), no. 4, pp. 557–578.CrossRefGoogle Scholar
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[5] Poizat, Bruno, Une tentative malheureuse de construire une structure eliminant rapidement les quanteurs, Lecture Notes in Computer Science, vol. 1862, 2000, pp. 61–70.Google Scholar
[6]Prunescu, Mihai, Non-effective quantifier elimination, Mathematical Logic Quarterly, vol. 47 (2001), no. 4, pp. 557–561.3.0.CO;2-O>CrossRefGoogle Scholar