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Formalising Szemerédi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions in Isabelle/HOL

Accepted version
Peer-reviewed

Type

Article

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Authors

Koutsoukou-Argyraki, Angeliki 
Paulson, Lawrence C 

Abstract

We have formalised Szemer'edi'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.

Description

Keywords

cs.LO, cs.LO, 05C35, 05A17, 11P81, 03B35, 68V15, 68V20, 68V35

Journal Title

Journal of Automated Reasoning

Conference Name

Journal ISSN

0168-7433

Volume Title

Publisher

Springer

Publisher DOI

Publisher URL

Sponsorship
European Research Council (742178)
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