Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP
Original language description
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 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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
R - Projekt Ramcoveho programu EK
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings - Symposium on Logic in Computer Science
ISBN
978-1-66544-895-6
ISSN
1043-6871
e-ISSN
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Number of pages
13
Pages from-to
1-13
Publisher name
The Institute of Electrical and Electronics Engineers (IEEE)
Place of publication
Itálie
Event location
Itálie
Event date
Jun 29, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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