2 Search Results for "Hales, Thomas C."


Document
Introduction to the Flyspeck Project

Authors: Thomas C. Hales

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)


Abstract
This article gives an introduction to a long-term project called Flyspeck, whose purpose is to give a formal verification of the Kepler Conjecture. The Kepler Conjecture asserts that the density of a packing of equal radius balls in three dimensions cannot exceed $pi/sqrt{18}$. The original proof of the Kepler Conjecture, from 1998, relies extensively on computer calculations. Because the proof relies on relatively few external results, it is a natural choice for a formalization effort.

Cite as

Thomas C. Hales. Introduction to the Flyspeck Project. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{hales:DagSemProc.05021.16,
  author =	{Hales, Thomas C.},
  title =	{{Introduction to the Flyspeck Project}},
  booktitle =	{Mathematics, Algorithms, Proofs},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5021},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.16},
  URN =		{urn:nbn:de:0030-drops-4329},
  doi =		{10.4230/DagSemProc.05021.16},
  annote =	{Keywords: Certified proofs, Kepler conjecture}
}
Document
Towards a Verified Enumeration of All Tame Plane Graphs

Authors: Tobias Nipkow and Gertrud Bauer

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)


Abstract
In his proof of the Kepler conjecture, Thomas Hales introduced the notion of tame graphs and provided a Java program for enumerating all tame plane graphs. We have translated his Java program into an executable function in HOL ("the generator"), have formalized the notions of tameness and planarity in HOL, and have partially proved that the generator returns all tame plane graphs. Running the generator in ML has shows that the list of plane tame graphs ("the archive") that Thomas Hales also provides is complete. Once we have finished the completeness proof for the generator. In addition we checked the redundancy of the archive by formalising an executable notion of isomorphism between plane graphs, and checking if the archive contains only graphs produced by the generator. It turned out that 2257 of the 5128 graphs in the archive are either not tame or isomorphic to another graph in the archive.

Cite as

Tobias Nipkow and Gertrud Bauer. Towards a Verified Enumeration of All Tame Plane Graphs. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{nipkow_et_al:DagSemProc.05021.21,
  author =	{Nipkow, Tobias and Bauer, Gertrud},
  title =	{{Towards a Verified Enumeration of All Tame Plane Graphs}},
  booktitle =	{Mathematics, Algorithms, Proofs},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5021},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.21},
  URN =		{urn:nbn:de:0030-drops-4343},
  doi =		{10.4230/DagSemProc.05021.21},
  annote =	{Keywords: Kepler conjecture, certified proofs, flyspeck}
}
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