Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras
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 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.
Czech name
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Czech description
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Classification
Type
J<sub>ost</sub> - Miscellaneous article in a specialist periodical
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
TheoretiCS
ISSN
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e-ISSN
2751-4838
Volume of the periodical
3
Issue of the periodical within the volume
15.5.2024
Country of publishing house
DE - GERMANY
Number of pages
76
Pages from-to
1-76
UT code for WoS article
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EID of the result in the Scopus database
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