FINITE ALGEBRAS WITH HOM-SETS OF POLYNOMIAL SIZE

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509210" target="_blank" >RIV/00216208:11320/25:10509210 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GNN2aokBOE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GNN2aokBOE</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/9262" target="_blank" >10.1090/tran/9262</a>

Result language
angličtina
Original language name
FINITE ALGEBRAS WITH HOM-SETS OF POLYNOMIAL SIZE
Original language description
We provide an internal characterization of those finite algebras(i.e., algebraic structures) A such that the number of homomorphisms fromany finite algebra X to A is bounded from above by a polynomial in the sizeof X. Namely, an algebra A has this property if, and only if, no subalgebraof A has a nontrivial strongly abelian congruence. We also show that theproperty can be decided in polynomial time for algebras in finite signatures.Moreover, if A is such an algebra, the set of all homomorphisms from X to Acan be computed in polynomial time given X as input. As an application ofour results to the field of computational complexity, we characterize inherentlytractable constraint satisfaction problems over fixed finite structures, i.e., thosethat are tractable and remain tractable after expanding the fixed structure byarbitrary relations or functions.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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