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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2021.22
URN: urn:nbn:de:0030-drops-139177
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13917/
Holub, Štěpán ;
Starosta, Štěpán
Formalization of Basic Combinatorics on Words
Abstract
Combinatorics on Words is a rather young domain encompassing the study of words and formal languages. An archetypal example of a task in Combinatorics on Words is to solve the equation x ⋅ y = y ⋅ x, i.e., to describe words that commute.
This contribution contains formalization of three important classical results in Isabelle/HOL. Namely i) the Periodicity Lemma (a.k.a. the theorem of Fine and Wilf), including a construction of a word proving its optimality; ii) the solution of the equation x^a ⋅ y^b = z^c with 2 ≤ a,b,c, known as the Lyndon-Schützenberger Equation; and iii) the Graph Lemma, which yields a generic upper bound on the rank of a solution of a system of equations.
The formalization of those results is based on an evolving toolkit of several hundred auxiliary results which provide for smooth reasoning within more complex tasks.
BibTeX - Entry
@InProceedings{holub_et_al:LIPIcs.ITP.2021.22,
author = {Holub, \v{S}t\v{e}p\'{a}n and Starosta, \v{S}t\v{e}p\'{a}n},
title = {{Formalization of Basic Combinatorics on Words}},
booktitle = {12th International Conference on Interactive Theorem Proving (ITP 2021)},
pages = {22:1--22:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-188-7},
ISSN = {1868-8969},
year = {2021},
volume = {193},
editor = {Cohen, Liron and Kaliszyk, Cezary},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13917},
URN = {urn:nbn:de:0030-drops-139177},
doi = {10.4230/LIPIcs.ITP.2021.22},
annote = {Keywords: combinatorics on words, formalization, Isabelle/HOL}
}
