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Logics which capture complexity classes over the reals

Published online by Cambridge University Press:  12 March 2014

Felipe Cucker and
Klaus Meer
Felipe Cucker
Affiliation:
Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong E-mail: macucker@sobolev.cityu.edu.hk
Klaus Meer
Affiliation:
Lehrstuhl c Für Mathematik, Rwth Aachen, D-52056 Aachen, Germany E-mail: meer@rwth-aachen.de
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Abstract

In this paper we deal with the logical description of complexity classes arising in the real number model of computation introduced by Blum, Shub, and Smale [4]. We adapt the approach of descriptive complexity theory for this model developped in [14] and extend it to capture some further complexity classes over the reals by logical means. Among the latter we find NCℝ, PARℝ, EXPℝ and some others more.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999, pp. 363 - 390
Copyright
Copyright © Association for Symbolic Logic 1999

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