http://www.dagstuhl.de/09471

15. – 20. November 2009, Dagstuhl Seminar 09471

Computer-assisted proofs - tools, methods and applications

Organisatoren

B. Malcolm Brown (Cardiff University, GB)
Erich Kaltofen (North Carolina State University – Raleigh, US)
Shin'ichi Oishi (Waseda University – Tokyo, JP)
Siegfried M. Rump (TU Hamburg-Harburg, DE)

Auskunft zu diesem Dagstuhl Seminar erteilt

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Dokumente

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Summary

Our seminars on computer-assisted proofs are intended to assemble a diverse group of scientists working on differing aspects of computer-assisted proofs and verification methods. The current one is the fifth initiated by Rump.

Computer-assisted proofs in general are characterized by the fact that part of a mathematical proof is assisted in an algorithmic way. This includes numerical calculations, taking account of all numerical errors, as well as symbolic computations.

This concept of computer-assisted proofs can be regarded as a special approach to constructive mathematics. In recent years, various mathematical problems have been solved by computer-assisted proofs, among then the Kepler conjecture (a 3 dimensional sphere packing problem), the existence of chaos, the existence of the Lorenz attractor, and more.

This concept of computer assisted proofs can be regarded as a special approach to constructive mathematics. In recent years, various mathematical problems have been solved by computer-assisted proofs, among then the Kepler conjecture (a 3 dimensional sphere packing problem), the existence of chaos, the existence of the Lorenz attractor, and more.

A major representative of computer-assisted proofs are so-called verification methods. These are algorithms verifying the correctness of the assumptions of mathematical theorems with rigor. These methods use solely floating-point arithmetic estimating all numerical errors. Therefore these methods are particularly fast. Besides the conference, a 163-page review article on verification methods by Rump was discussed which appeared in 2010 in Acta Numerica.

The organizers refrained from presenting talks to give more space to the participants. As always, they and the 46 participants from 10 different countries of the seminar enjoyed the pleasant and stimulating atmosphere in Dagstuhl. Our own assessment is that computer-assisted proofs have several new exciting directions pursued by a number of established and young researchers, and we are already looking forward to the next seminar.

Related Dagstuhl Seminar

Classification

  • Verification / Logic
  • Semantics / Formal Methods

Keywords

  • Computer-assisted proofs
  • Verification methods
  • Error-free transformations
  • Computer algebra
  • Semidefinite programming

Buchausstellung

Bücher der Teilnehmer 

Buchausstellung im Erdgeschoss der Bibliothek

(nur in der Veranstaltungswoche).

Dokumentation

In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.

 

Download Übersichtsflyer (PDF).

Publikationen

Es besteht weiterhin die Möglichkeit, eine umfassende Kollektion begutachteter Arbeiten in der Reihe Dagstuhl Follow-Ups zu publizieren.

Dagstuhl's Impact

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