Edmonds, C. orcid.org/0000-0002-8559-9133, Koutsoukou-Argyraki, A. orcid.org/0000-0002-8886-5281
and Paulson, L.C. orcid.org/0000-0003-0288-4279
(2022)
Formalising Szemerédi’s regularity lemma and Roth’s theorem on arithmetic progressions in Isabelle/HOL.
Journal of Automated Reasoning, 67.
2.
ISSN 0168-7433
Abstract
We have formalised Szemerédi’s Regularity Lemma and Roth’s Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant Isabelle/HOL. For the latter formalisation, we used the former to first show the Triangle Counting Lemma and the Triangle Removal Lemma: themselves important technical results. Here, in addition to showcasing the main formalised statements and definitions, we focus on sensitive points in the proofs, describing how we overcame the difficulties that we encountered.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Interactive theorem proving; Proof assistant; Formalisation of mathematics; Isabelle/HOL; Additive combinatorics; Extremal graph theory; Arithmetic progressions; Number theory |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Jan 2024 11:45 |
Last Modified: | 12 Jan 2024 11:45 |
Published Version: | http://dx.doi.org/10.1007/s10817-022-09650-2 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s10817-022-09650-2 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207528 |