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By Jens Blanck (auth.), Jens Blanck, Vasco Brattka, Peter Hertling (eds.)

The workshop on Computability and Complexity in research, CCA 2000, was once hosted via the dep. of computing device technological know-how of the college of Wales Swansea, September 17{19, 2000. It was once the fourth workshop in a profitable sequence of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. approximately forty contributors from the nations uk, Germany, Japan, Italy, Russia, France, Denmark, Greece, and eire contributed to the good fortune of this assembly. Altogether, 28 talkswere p- sented in Swansea. those lawsuits contain 23 papers which signify a cro- part via fresh learn on computability and complexity in research. The workshop succeeded in bringing jointly humans attracted to computability and complexity facets of study and in exploring connections with nume- cal tools, physics and, after all, desktop technology. It used to be rounded o by means of a few talks and papers on special machine mathematics and by means of a contest of v e applied platforms. A document in this festival has been incorporated in those court cases. we wish to thank the authors for his or her contributions and the referees for his or her cautious paintings, and we are hoping for additional inspiring and optimistic conferences of an identical type. April 2001 Jens Blanck Vasco Brattka Peter Hertling association CCA2000was hosted through the dept of laptop technology of the collage of Wales Swansea and came about on September 17{19, 2000.

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Additional resources for Computability and Complexity in Analysis: 4th International Workshop, CCA 2000 Swansea, UK, September 17–19, 2000 Selected Papers

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Matula. An algorithm for redundant binary bit-pipelined rational arithmetic. IEEE Transactions on Computers, 39(8):1106–1115, 1990. Ker-I Ko. On the continued fraction representation of computable real numbers. Theoretical Computer Science, 47:299–313, 1986. corr. , Vol. 54 (1987), Pages 341–343. 46 Paul Gowland and David Lester Ko91. Kr¨ a98. Lac55a. Lac55b. Lac55c. Lac58. LB90. Les01. LL90. Mar54. MM94. Mos57. M¨ ul86. M¨ ul98. Mul00a. M¨ ul00b. Myh72. PER89. Ker-I Ko. Complexity Theory of Real Functions.

Springer, Berlin, 1987. Klaus Weihrauch. Computable Analysis. Springer, Berlin, 2000. Klaus Weihrauch and Christoph Kreitz. Representations of the real numbers and of the open subsets of the set of real numbers. Annals of Pure and Applied Logic, 35:247–260, 1987. P. Zimmermann. MPFR: A library for multiprecision floating-point arithmetic with exact rounding. In Fourth Conference on Real Numbers and Computers, pages 89–90, Schloss Dagstuhl, Saarland, Germany, April 2000. Standard Representations of Effective Metric Spaces Armin Hemmerling Ernst-Moritz-Arndt-Universit¨ at Greifswald Institut f¨ ur Mathematik und Informatik Friedrich-Ludwig-Jahn-Str.

As stated in the paper “Although the data are exactly representable and only 5 floating point operations are done, the computed “solution” has nothing to do with the exact solution”. 3 Theoretical Approaches to the Real Numbers In many approaches to computable analysis, for example those of Grzegorczyk [Grz55,Grz57,Grz59], Ko [Ko91], Lacombe [Lac55a,Lac55b,Lac55c,Lac58], PourEl and Richards [PER89], and Weihrauch [Wei00], we are able to investigate computable functions over arbitrary real numbers.

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