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Abstract: We present a logical approach to complexity over the real numbers with respect to the model of Blum, Shub and Smale. The logics under consideration are interpreted over a special class of twosorted structures, called R-structures: They consist of a finite structure together with the ordered field of reals and a finite set of functions from the finite structure into R. They are a special case of the metafinite structures introduced recently by Grädel and Gurevich. We argue that R-structures... (Update)
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BibTeX entry: (Update)
E. Gradel and K. Meer. Descriptive complexity theory over the real numbers. In J. Renegar, M. Shub, and S. Smale, editors, The Mathematics of Numerical Analysis, volume 32 of Lectures in Applied Mathematics, pages 381--404. American Mathematical Society, 1996. http://citeseer.ist.psu.edu/gradel96descriptive.html More
@incollection{ gradel96descriptive,
author = "Gr{\"a}del and Meer",
title = "Descriptive Complexity Theory over the Real Numbers",
booktitle = "The Mathematics of Numerical Analysis: 1995 (25th) {AMS}-{SIAM} Summer Seminar in Applied Mathematics (Lectures in Applied Mathematics, Volume 32), American Mathematical Society",
editor = "Renegar and Shub and Smale",
year = "1996",
url = "citeseer.ist.psu.edu/gradel96descriptive.html" }
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294 Finite Model Theory (context) - Ebbinghaus, Flum - 1995
245 Relational queries computable in polynomial time - Immerman - 1986
213 a theory of computation and complexity over the real numbers.. (context) - Blum, Shub et al. - 1989
211 Languages that Capture Complexity Classes - Immerman - 1987
210 Generalized first-order spectra and polynomial-time recogniz.. (context) - Fagin - 1974
149 Logic and the Challenge of Computer Science (context) - Gurevich - 1988
128 Complexity and Real Computation (context) - Blum, Cucker et al.
61 Descriptive and Computational Complexity - Immerman - 1989
58 Algebraic Complexity Theory (context) - Burgisser, Clausen et al.
27 Algebraic Complexity Theory (context) - Strassen - 1990
19 Polynomial computability and recursivity in finite domains (context) - Sazonov - 1980
17 Reductions to NP-Complete Problems by Interpretations (context) - Dahlhaus - 1983
16 Algebraic Complexity Theory (context) - Gathen - 1988
15 the Power of real Turing Machines over Binary Inputs - Cucker, Grigoriev - 1994
12 On semialgebraic decision complexity (context) - Lickteig - 1990
11 the Complexity of Quadratic Programming in Real Number Model.. (context) - Meer - 1994
11 Metafinite Model Theory - Gradel, Gurevich - 1995
10 Capturing Complexity Classes by Fragments of Second Order Lo.. (context) - Gradel - 1992
9 Separation of Complexity Classes in Koiran's weak model (context) - Cucker, Shub et al. - 1994
6 Journal of Complexity (context) - Cucker, NCR - 1992
5 complete Problems in the Theory of the Reals (context) - Cucker, Torrecillas et al. - 1992
4 Zeitschrift fur mathematische Logik und Grundlagen der Mathe.. (context) - G'acs, Lov'asz et al. - 1977
3 a propos des machines sur R introduites par Blum, Shub et Sm.. (context) - Michaux, remarque - 1989
3 A weak version of the Blum-Shub-Smale model - Koiran - 1993
1 A Survey on Structural Real Complexity Theory (context) - Meer, Michaux - 1995
1 Expressibility as a Complexity Measure (context) - Immerman - 1987
1 th IEEE Symposium on Foundations of Computer Science (context) - Gurevich, feasible et al. - 1983
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