TOPOLOGY IS IRRELEVANT (IN A DICHOTOMY CONJECTURE FOR INFINITE DOMAIN CONSTRAINT SATISFACTION PROBLEMS)
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421064" target="_blank" >RIV/00216208:11320/20:10421064 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qhDISn9fvW" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qhDISn9fvW</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/18M1216213" target="_blank" >10.1137/18M1216213</a>
Alternative languages
Result language
angličtina
Original language name
TOPOLOGY IS IRRELEVANT (IN A DICHOTOMY CONJECTURE FOR INFINITE DOMAIN CONSTRAINT SATISFACTION PROBLEMS)
Original language description
( )The tractability conjecture for finite domain constraint satisfaction problems (CSPs) stated that such CSPs are solvable in polynomial time whenever there is no natural reduction, in some precise technical sense, from the 3-SAT problem; otherwise, they are NP-complete. Its recent resolution draws on an algebraic characterization of the conjectured borderline: the CSP of a finite structure permits no natural reduction from 3-SAT if and only if the stabilizer of the polymorphism clone of the core of the structure satisfies some nontrivial system of identities, and such satisfaction is always witnessed by several specific nontrivial systems of identities which do not depend on the structure. The tractability conjecture has been generalized in the above formulation to a certain class of infinite domain CSPs, namely, CSPs of reducts of finitely bounded homogeneous structures. It was subsequently shown that the conjectured borderline between hardness and tractability, i.e., a natural reduction from 3-SAT, can be characterized for this class by a combination of algebraic and topological properties. However, it was not known whether the topological component is essential in this characterization. We provide a negative answer to this question by proving that the borderline is characterized by one specific algebraic identity, namely, the pseudo-Siggers identity alpha s(x, y, x, z, y, z) approximate to beta s(y, x, z, x, z, y). This accomplishes one of the steps of a proposed strategy for reducing the infinite domain CSP dichotomy conjecture to the finite case. Our main theorem is also of independent mathematical interest, characterizing a topological property of any omega-categorical core structure (the existence of a continuous homomorphism of a stabilizer of its polymorphism clone to the projections) in purely algebraic terms (the failure of an identity as above).
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GA13-01832S" target="_blank" >GA13-01832S: General algebra and its connections to computer science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Computing
ISSN
0097-5397
e-ISSN
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Volume of the periodical
2020
Issue of the periodical within the volume
49
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
365-393
UT code for WoS article
000546873800004
EID of the result in the Scopus database
2-s2.0-85084414747