http://www.dagstuhl.de/09471

November 15 – 20 , 2009, Dagstuhl Seminar 09471

Computer-assisted proofs - tools, methods and applications

Organizers

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)


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Dagstuhl Service Team

Documents

Dagstuhl Seminar Proceedings DROPS
List of Participants

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

Book exhibition

Books from the participants of the current Seminar 

Book exhibition in the library, ground floor, during the seminar week.

Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.

 

Download overview leaflet (PDF).

Publications

Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.