Binary codes that do not preserve primitivity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471775" target="_blank" >RIV/00216208:11320/23:10471775 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YraEb5m23M" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YraEb5m23M</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Binary codes that do not preserve primitivity
Original language description
A code χ is not primitivity preserving if there is a primitive list ws ε lists χ whose concatenation is imprimitive. We formalize a full characterization of such codes in the binary case in the proof assistant Isabelle/HOL. Part of the formalization, interesting on its own, is a description of {x,y}- interpretations of the square xx if lenght y <= lenght x. We also provide a formalized parametric solution of the related equation x(j) y(k) = z(l).The core of the theory is an investigation of imprimitive words which are concatenations of copies of two noncommuting words (such a pair of words is called a binary code). We follow the article [Barbin-Le Rest, Le Rest, 85] (mainly Théorème 2.1 and Lemme 3.1), while substantially optimizing the proof. See also [J.-C. Spehner. Quelques problèmes d'extension, de conjugaison et de présentation des sous-monoïdes d'un monoïde libre. PhD thesis, Université Paris VII, 1976] for an earlier result on this question, and [Maňuch, 01] for another proof.
Czech name
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Czech description
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Project
<a href="/en/project/GA20-20621S" target="_blank" >GA20-20621S: Combinatorics on words formalization</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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