Dagstuhl Seminar on
Computability and Complexity in Analysis 2001

It takes place at Schloß Dagstuhl, Wadern, Germany, November 11-16, 2001.

Motivation

This Dagstuhl seminar is concerned with the theory of computability and complexity over the real numbers which is built on the Turing machine model. This theory was initiated by Turing, Grzegorczyk, Lacombe, Banach and Mazur, and has seen a rapid growth in recent years. Recent monographs are by Pour-El/Richards, Ko, and Weihrauch.

Computability theory and complexity theory are two central areas of research in theoretical computer science. Until recently, most work in these areas concentrated on problems over discrete structures. In the last years, though, there has been an enormous growth of computability theory and complexity theory over the real numbers and other continuous structures. One of the reasons for this phenomenon is that more and more practical computation problems over the real numbers are being dealt with by computer scientists, for example, in computational geometry, in the modelling of dynamical and hybrid systems, but also in classical problems from numerical mathematics. The scientists working on these questions come from different fields, such as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics, analysis etc.

The Dagstuhl seminar provides a unique opportunity for people from such diverse areas to meet and exchange ideas and knowledge. One of the topics of interest is foundational work concerning the various models and approaches for defining or describing computability and complexity over the real numbers. We also hope to gain new insights into the computability-theoretic side of various computational questions from physics as well as from other fields involving computations over the real numbers. This, of course, also requires the extension of existing computability notions to more general classes of objects. Other topics of interest are complexity-theoretic investigations, both foundational and with respect to concrete problems. Last but not least, new implementations of exact real arithmetic and further developments of already existing software packages will be of interest.

Participants

• Götz Alefeld, Universität Karlsruhe, Germany,
  On the Theorems of Kantorovich, Moore, and Miranda
• Klaus Ambos-Spies, Universität Heidelberg, Germany
• Goerge Barmpalias, University of Leeds, UK
• Andrej Bauer, IMFM Ljubiljana, Slovenia,
  On the Relationship between Domain Theory and Type Two Effectivity
• Markus Bläser, Medizinische Universität Lübeck, Germany,
  Weierstrass Approximation Theorems for NP and #P Real Functions
• Vasco Brattka, Universität Hagen, Germany,
  Computable Versions of the Closed Graph and the Open Mapping Theorem
• Douglas Bridges, University of Canterbury - Christchurch, New Zealand,
  Apartness spaces as a foundation for constructive topology
• Douglas Cenzer, University of Florida - Gainesville, USA,
  Effectively Closed Sets and Graphs of Computable Real Functions
• Rod Downey, University of Wellington, New Zealand,
  Reals and Randomness
• Martin H. Escardo, University of Birmingham, UK,
  A universal characterization of the Euclidean unit interval
• Tobias Gärtner, Universität Saarbrücken, Germany
• Magne Haveraaen, University of Bergen, Norway,
  Computational Scalar Fields - A Basis for Partial Differential Equations
• Armin Hemmerling, Universität Greifswald, Germany,
  Approximate Decidability
• Peter Hertling, Universität Hagen, Germany,
  Random sets versus random sequences
• Denis Hirschfeldt, University of Chicago, USA,
  Relative 1-Randomess of Reals
• Elham Kashefi, Imperial College - London, UK,
  Quantum Oracle Complexity
• Ulrich Kohlenbach, BRICS - Aarhus, Denmark,
  Proof mining in numerical analysis: effective strong unicity in L₁-approximation
• Michal Konecny, University of Edinburgh, UK,
  Continuity of Non-Extensional Computation
• Margarita Korovina, Sobolev Institute of Mathematics - Novosibirsk, Russia,
  Higher Order Computability over the Real Numbers
• Marko Krznaric, Imperial College - London, UK,
  Domain Theory and Differential Calculus
• Oleg V. Kudinov, Sobolev Institute of Mathematics - Novosibirsk, Russia,
  P-Time Computable Reals and some Complexity Classes
• David Lester, Manchester University, UK,
  Infinite Precision Basic Linear Algebra Systems or Why Norbert Müller is Right
• Peter Lietz, TU Darmstadt, Germany,
  TTE via Kleene's Function Realizability
• Klaus Meer, Univ. of Southern Denmark - Odense, Denmark,
  A step towards a complexity theory for dynamical systems
• Joseph S. Miller, Cornell University, USA,
  The Sets Fixable by Computable Maps on the n-Ball
• Takakazu Mori, Kyoto-Sangyo University, Japan,
  Fine Computable Functions and Their Walsh Fourier Coefficients
• Norbert Müller, Universität Trier, Germany,
  Real Numbers and BDDs
• Dag Normann, University of Oslo, Norway
• Paulo Oliva, BRICS - Aarhus, Denmark,
  On the Computational Complexity of L₁-Approximation
• Robert Rettinger, Universität Hagen, Germany
• Matthias Schröder, Universität Hagen, Germany,
  Effectivity in Admissibly Representable Spaces
• Peter M. Schuster, Universität München, Germany,
  Compactness in constructive analysis
• Victor Selivanov, Pedagogical University - Novosibirsk, Russia
• Olha Shkaravska, Materialise Ukraine - Kiew, Ukraine
• Alex Simpson, University of Edinburgh, UK,
  Comparing Functional Paradigms for Exact Real Arithmetic
• Dimiter Skordev, University of Sofia, Bulgaria,
  Well Computable Real Numbers
• Bas Spitters, University of Nijmegen, Netherlands
  Unbounded Operators on Hilbert Spaces in Constructive Mathematics
• Ludwig Staiger, Universität Halle-Wittenberg, Germany,
  Properties of real interpretations of omega-words
• Izumi Takeuti, Kyoto University, Japan,
  Representations of Functionals
• Hideki Tsuiki, Kyoto University, Japan,
  A domain-theoretic account of computability via bottomed sequences
• Klaus Weihrauch, Universität Hagen, Germany,
  Computational Complexity on Computable Metric Spaces
• Mariko Yasugi, Kyoto-Sangyo University, Japan,
  Metrization of the uniform space and effective convergence
• Atsushi Yoshikawa, Kyushu University, Japan,
  Computability and Entropy Solutions of Conservation Laws
• Xizhong Zheng, BTU Cottbus, Germany,
  Beyond Computable Real Numbers
• Ning Zhong, University of Cincinnati, USA,
  Computable Analysis of Partial Differential Equations
• Martin Ziegler, Universität Paderborn, Germany,
  Computability on regular subsets of Euclidean space

Proceedings

It is planned to publish a special issue of Mathematical Logic Quarterly (MLQ), dedicated to the CCA Dagstuhl Seminar. This issue will include a limited number of full-length papers which must meet scope and standards of MLQ. There will be no page limit for individual papers, but there is a total limit of 160 pages for the whole issue. Thus, extraordinarily long papers might not be included. Submission deadline: December 31, 2001 Notification: March 15, 2002 Final papers: April 15, 2002 Electronical submissions (PostScript files) are welcome. For the final version LaTeX files are required. For the preparation of your submission please use the following LaTeX header or LaTeX2e header. Or you can already use the MLQ Style Files which have to be used for the final versions of papers. The special issue is scheduled to appear as Volume 48 (2002) Supplement 1.

Abstracts

During the seminar participants will be asked to use the following example to create an electronical version of an abstract of their talk and send send it to Michal Konecny. This abstract will be included in the Dagstuhl Seminar Report.

A participant's viewpoint

Picture based on slides of Andrej Bauer.