Existence of cube terms in finite algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438457" target="_blank" >RIV/00216208:11320/21:10438457 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0H.d4Pj-Js" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0H.d4Pj-Js</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-020-00700-7" target="_blank" >10.1007/s00012-020-00700-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence of cube terms in finite algebras

Popis výsledku v původním jazyce

We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if such an algebra has a cube term then it has a cube term of dimension at most N, where the number N depends on the arities of basic operations of the algebra and the size of the basic set. For finite idempotent algebras we give a tight bound on N that, in the special case of algebras with more than ((vertical bar A vertical bar)(2)) basic operations, improves an earlier result of K. Kearnes and a. Szendrei. On the algorithmic side, we show that deciding the existence of cube terms is in P for idempotent algebras and in EXPTIME in general. Since an algebra contains a k-ary near unanimity operation if and only if it contains a k-dimensional cube term and generates a congruence distributive variety, our algorithm also lets us decide whether a given finite algebra has a near unanimity operation.

Název v anglickém jazyce

Existence of cube terms in finite algebras

Popis výsledku anglicky

We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if such an algebra has a cube term then it has a cube term of dimension at most N, where the number N depends on the arities of basic operations of the algebra and the size of the basic set. For finite idempotent algebras we give a tight bound on N that, in the special case of algebras with more than ((vertical bar A vertical bar)(2)) basic operations, improves an earlier result of K. Kearnes and a. Szendrei. On the algorithmic side, we show that deciding the existence of cube terms is in P for idempotent algebras and in EXPTIME in general. Since an algebra contains a k-ary near unanimity operation if and only if it contains a k-dimensional cube term and generates a congruence distributive variety, our algorithm also lets us decide whether a given finite algebra has a near unanimity operation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Algebra Universalis

ISSN

0002-5240

e-ISSN

—

Svazek periodika

82

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

29

Strana od-do

11

Kód UT WoS článku

000610553000002

EID výsledku v databázi Scopus

2-s2.0-85099356936