The wonderland of reflections

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10383370" target="_blank" >RIV/00216208:11320/18:10383370 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11856-017-1621-9" target="_blank" >https://doi.org/10.1007/s11856-017-1621-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11856-017-1621-9" target="_blank" >10.1007/s11856-017-1621-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The wonderland of reflections

Popis výsledku v původním jazyce

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable omega-categorical relational structures have two algebraic counterparts for their polymorphism clones: a semantic one via the standard algebraic operators H, S, P, and a syntactic one via clone homomorphisms (capturing identities). We provide a similar characterization which incorporates all relational constructions relevant for CSPs, that is, homomorphic equivalence and adding singletons to cores in addition to ppinterpretations. For the semantic part we introduce a new construction, called reflection, and for the syntactic part we find an appropriate weakening of clone homomorphisms, called h1 clone homomorphisms (capturing identities of height 1). As a consequence, the complexity of the CSP of an at most countable omega-categorical structure depends only on the identities of height 1 satisfied in its polymorphism clone as well as the natural uniformity thereon. This allows us in turn to formulate a new elegant dichotomy conjecture for the CSPs of reducts of finitely bounded homogeneous structures. Finally, we reveal a close connection between h1 clone homomorphisms and the notion of compatibility with projections used in the study of the lattice of interpretability types of varieties.

Název v anglickém jazyce

The wonderland of reflections

Popis výsledku anglicky

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable omega-categorical relational structures have two algebraic counterparts for their polymorphism clones: a semantic one via the standard algebraic operators H, S, P, and a syntactic one via clone homomorphisms (capturing identities). We provide a similar characterization which incorporates all relational constructions relevant for CSPs, that is, homomorphic equivalence and adding singletons to cores in addition to ppinterpretations. For the semantic part we introduce a new construction, called reflection, and for the syntactic part we find an appropriate weakening of clone homomorphisms, called h1 clone homomorphisms (capturing identities of height 1). As a consequence, the complexity of the CSP of an at most countable omega-categorical structure depends only on the identities of height 1 satisfied in its polymorphism clone as well as the natural uniformity thereon. This allows us in turn to formulate a new elegant dichotomy conjecture for the CSPs of reducts of finitely bounded homogeneous structures. Finally, we reveal a close connection between h1 clone homomorphisms and the notion of compatibility with projections used in the study of the lattice of interpretability types of varieties.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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

2018

Kód důvěrnosti údajů

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

Název periodika

Israel Journal of Mathematics

ISSN

0021-2172

e-ISSN

—

Svazek periodika

223

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IL - Stát Izrael

Počet stran výsledku

36

Strana od-do

363-398

Kód UT WoS článku

000427197200011

EID výsledku v databázi Scopus

2-s2.0-85035759181