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Accessible telephone directories

Published online by Cambridge University Press:  12 March 2014

John B. Goode
John B. Goode*
Affiliation:
Université Claude Bernard (Lyon-1), Mathématiques, Bâtiment 101, 69622 Villeurbanne-Cédex, FranceE-mail:, [email protected].
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Abstract

We reduce to a standard circuit-size complexity problem a relativisation of the P=NP question that we believe to be connected with the same question in the model for computation over the reals defined by L. Blum. M. Shub, and S. Smale. On this occasion, we set the foundations of a general theory for computation over an arbitrary structure, extending what these three authors did in the case of rings.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 92 - 105
Copyright
Copyright © Association for Symbolic Logic 1994

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References

[BP 1988]Bouscaren, Elisabeth and Poizat, Bruno, Des belles paires aux beaux uples, this Journal, vol. 53, pp. 434–442.Google Scholar
[BSS 1989]Blum, Lenore, Shub, Mike and Smale, Steve, On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions, and universal machines, Bulletin of the American Mathematical Society, vol. 21, pp. 1–46.CrossRefGoogle Scholar
[S 1990]Stern, Jacques, Fondements mathématiques de l'Informatique: logique et complexité, McGraw-Hill, Paris.Google Scholar