The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems

Popis výsledku anglicky

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).

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA13-01832S" target="_blank" >GA13-01832S: Obecná algebra a její souvislost s informatikou</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

PROCEEDINGS OF THE 31ST ANNUAL ACM-IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS 2016)

ISBN

978-1-4503-4391-6

ISSN

—

e-ISSN

—

Počet stran výsledku

8

Strana od-do

615-622

Název nakladatele

ASSOC COMPUTING MACHINERY

Místo vydání

NEW YORK

Místo konání akce

New York City

Datum konání akce

5. 7. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000387609200062