The algebraic 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%2F16%3A10331272" target="_blank" >RIV/00216208:11320/16:10331272 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1145/2933575.2934544" target="_blank" >http://dx.doi.org/10.1145/2933575.2934544</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/2933575.2934544" target="_blank" >10.1145/2933575.2934544</a>
Alternative languages
Result language
angličtina
Original language name
The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems
Original language description
We prove that an omega-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that this happens if and only if its polymorphism clone does not contain operations alpha,beta, s satisfying the identity alpha s(x, y, x, z, y, z) approximate to beta s( y, x, z, x, z, y). This establishes an algebraic criterion equivalent to the conjectured boderline between P and NP-complete CSPs over reducts of finitely bounded homogenous structures, and accomplishes one of the steps of a proposed strategy for reducing the infinite domain CSP dichotomy conjecture to the finite case. Our 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
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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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
2016
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 OF THE 31ST ANNUAL ACM-IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS 2016)
ISBN
978-1-4503-4391-6
ISSN
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e-ISSN
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Number of pages
8
Pages from-to
615-622
Publisher name
ASSOC COMPUTING MACHINERY
Place of publication
NEW YORK
Event location
New York City
Event date
Jul 5, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000387609200062