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21st Days of Weak Arithmetics
June 7-9, 2002
Steklov Institute of Mathematics
St. Petersburg, Russia

Organizers
Paola d'Aquino (Italy), Anatoly Beltiukov (Russia), Patrick Cegielski (France), Gregory Kucherov (France), Krzysztof Lorys (Poland), Yuri Matiyassevich (Russia), the chairman, Jean-Pierre Ressayre (France), Denis Richard (France), Maxim Vsemirov (Russia)

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Equivalence of Scalar- and Vector-recursion for BSS Machines
by
Christophe Troestler
University of Mons-Hainaut, Belgium

In the end of the nineties, L. Blum, M. Shub and S. Smale developed their famous model of machines that are able to perform computations directly on the real numbers. The set of functions that are computable for this model can also be described as the closure of some set of basic functions under four operations (composition, juxtaposition, recursion, minimalization). Recursion can be used with scalar- or (a priori more powerfully) with vector-valued functions. In this talk, we will show that, despite the fact that R is not computably isomorphic to RN when N =/= 1, the classes generated by scalar- and vector-recursion are generally the same. We will also discuss the non-equality case.

Date received: June 2, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cail-24.