WHEN SYMMETRIES ARE NOT ENOUGH: A HIERARCHY OF HARD CONSTRAINT SATISFACTION PROBLEMS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452373" target="_blank" >RIV/00216208:11320/22:10452373 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ah9yRIa7N3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ah9yRIa7N3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/20M1383471" target="_blank" >10.1137/20M1383471</a>

Jazyk výsledku

angličtina

Název v původním jazyce

WHEN SYMMETRIES ARE NOT ENOUGH: A HIERARCHY OF HARD CONSTRAINT SATISFACTION PROBLEMS

Popis výsledku v původním jazyce

We produce a class of w-categorical structures with finite signature by applying a model-theoretic construction---a refinement of the Hrushovski-enco ding---to w-categorical structures in a possibly infinite signature. We show that the encoded structures retain desirable algebraic properties of the original structures, but that the constraint satisfaction problems (CSPs) associated with these structures can be badly behaved in terms of computational complexity. This method allows us to systematically generate w-categorical templates whose CSPs are complete for a variety of complexity classes of arbitrarily high complexity and w-categorical templates that show that membership in any given complexity class containing AC0 cannot be expressed by a set of identities on the polymorphisms. It moreover enables us to prove that recent results about the relevance of topology on polymorphism clones of w-categorical structures also apply for CSP templates, i.e., structures in a finite language. Finally, we obtain a concrete algebraic criterion which could constitute a description of the delineation between tractability and NP-hardness in the dichotomy conjecture for first-order reducts of finitely bounded homogeneous structures.

Název v anglickém jazyce

WHEN SYMMETRIES ARE NOT ENOUGH: A HIERARCHY OF HARD CONSTRAINT SATISFACTION PROBLEMS

Popis výsledku anglicky

We produce a class of w-categorical structures with finite signature by applying a model-theoretic construction---a refinement of the Hrushovski-enco ding---to w-categorical structures in a possibly infinite signature. We show that the encoded structures retain desirable algebraic properties of the original structures, but that the constraint satisfaction problems (CSPs) associated with these structures can be badly behaved in terms of computational complexity. This method allows us to systematically generate w-categorical templates whose CSPs are complete for a variety of complexity classes of arbitrarily high complexity and w-categorical templates that show that membership in any given complexity class containing AC0 cannot be expressed by a set of identities on the polymorphisms. It moreover enables us to prove that recent results about the relevance of topology on polymorphism clones of w-categorical structures also apply for CSP templates, i.e., structures in a finite language. Finally, we obtain a concrete algebraic criterion which could constitute a description of the delineation between tractability and NP-hardness in the dichotomy conjecture for first-order reducts of finitely bounded homogeneous structures.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-20123S" target="_blank" >GA18-20123S: Rozšíření záběru univerzální algebry</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Computing

ISSN

0097-5397

e-ISSN

1095-7111

Svazek periodika

2022

Číslo periodika v rámci svazku

51

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

175-213

Kód UT WoS článku

000776377400001

EID výsledku v databázi Scopus

2-s2.0-85128646965