Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438452" target="_blank" >RIV/00216208:11320/21:10438452 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1109/LICS52264.2021.9470557" target="_blank" >https://doi.org/10.1109/LICS52264.2021.9470557</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/LICS52264.2021.9470557" target="_blank" >10.1109/LICS52264.2021.9470557</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP

Popis výsledku v původním jazyce

This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to study the CSP over finite templates - absorption theory that was used to characterize CSPs solvable by local consistency methods (JACM&apos;14), and Bulatov&apos;s and Zhuk&apos;s theories that were used for two independent proofs of the CSP Dichotomy Theorem (FOCS&apos;17, JACM&apos;20). As the first contribution we present an elementary theorem about primitive positive definability and use it to obtain the starting points of Bulatov&apos;s and Zhuk&apos;s proofs as corollaries. As the second contribution we propose and initiate a systematic study of minimal Taylor algebras. This class of algebras is broad enough so that it suffices to verify the CSP Dichotomy Theorem on this class only, but still is unusually well behaved. In particular, many concepts from the three approaches coincide in the class, which is in striking contrast with the general setting. We believe that the theory initiated in this paper will eventually result in a simple and more natural proof of the Dichotomy Theorem that employs a simpler and more efficient algorithm, and will help in attacking complexity questions in other CSP-related problems.

Název v anglickém jazyce

Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP

Popis výsledku anglicky

This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to study the CSP over finite templates - absorption theory that was used to characterize CSPs solvable by local consistency methods (JACM&apos;14), and Bulatov&apos;s and Zhuk&apos;s theories that were used for two independent proofs of the CSP Dichotomy Theorem (FOCS&apos;17, JACM&apos;20). As the first contribution we present an elementary theorem about primitive positive definability and use it to obtain the starting points of Bulatov&apos;s and Zhuk&apos;s proofs as corollaries. As the second contribution we propose and initiate a systematic study of minimal Taylor algebras. This class of algebras is broad enough so that it suffices to verify the CSP Dichotomy Theorem on this class only, but still is unusually well behaved. In particular, many concepts from the three approaches coincide in the class, which is in striking contrast with the general setting. We believe that the theory initiated in this paper will eventually result in a simple and more natural proof of the Dichotomy Theorem that employs a simpler and more efficient algorithm, and will help in attacking complexity questions in other CSP-related problems.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

R - Projekt Ramcoveho programu EK

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings - Symposium on Logic in Computer Science

ISBN

978-1-66544-895-6

ISSN

1043-6871

e-ISSN

—

Počet stran výsledku

13

Strana od-do

1-13

Název nakladatele

The Institute of Electrical and Electronics Engineers (IEEE)

Místo vydání

Itálie

Místo konání akce

Itálie

Datum konání akce

29. 6. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—