Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489331" target="_blank" >RIV/00216208:11320/24:10489331 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ECRQd1vhlv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ECRQd1vhlv</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.48550/arXiv.2104.11808" target="_blank" >10.48550/arXiv.2104.11808</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras
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'14), and Bulatov's and Zhuk's theories that were used for two independent proofs of the CSP Dichotomy Theorem (FOCS'17, JACM'20). As the first contribution we present an elementary theorem about primitive positive definability and use it to obtain the starting points of Bulatov's and Zhuk'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 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 this 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
Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras
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'14), and Bulatov's and Zhuk's theories that were used for two independent proofs of the CSP Dichotomy Theorem (FOCS'17, JACM'20). As the first contribution we present an elementary theorem about primitive positive definability and use it to obtain the starting points of Bulatov's and Zhuk'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 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 this 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.
Klasifikace
Druh
J<sub>ost</sub> - Ostatní články v recenzovaných periodicích
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
TheoretiCS
ISSN
—
e-ISSN
2751-4838
Svazek periodika
3
Číslo periodika v rámci svazku
15.5.2024
Stát vydavatele periodika
DE - Spolková republika Německo
Počet stran výsledku
76
Strana od-do
1-76
Kód UT WoS článku
—
EID výsledku v databázi Scopus
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