Formalization of Basic Combinatorics on Words

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00350382" target="_blank" >RIV/68407700:21240/21:00350382 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10438465

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.ITP.2021.22" target="_blank" >https://doi.org/10.4230/LIPIcs.ITP.2021.22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ITP.2021.22" target="_blank" >10.4230/LIPIcs.ITP.2021.22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Formalization of Basic Combinatorics on Words

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Formalization of Basic Combinatorics on Words

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA20-20621S" target="_blank" >GA20-20621S: Formalizace kombinatoriky na slovech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

12th International Conference on Interactive Theorem Proving (ITP 2021)

ISBN

978-3-95977-188-7

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

17

Strana od-do

"22:1"-"22:17"

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl

Místo konání akce

Rome

Datum konání akce

29. 6. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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