Short Definitions in Constraint Languages

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471838" target="_blank" >RIV/00216208:11320/23:10471838 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.MFCS.2023.28" target="_blank" >https://doi.org/10.4230/LIPIcs.MFCS.2023.28</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2023.28" target="_blank" >10.4230/LIPIcs.MFCS.2023.28</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Short Definitions in Constraint Languages

Popis výsledku v původním jazyce

A first-order formula is called primitive positive (pp) if it only admits the use of existential quantifiers and conjunction. Pp-formulas are a central concept in (fixed-template) constraint satisfaction since CSP(Γ) can be viewed as the problem of deciding the primitive positive theory of Γ, and pp-definability captures gadget reductions between CSPs. An important class of tractable constraint languages Γ is characterized by having few subpowers, that is, the number of n-ary relations pp-definable from Γ is bounded by 2^p(n) for some polynomial p(n). In this paper we study a restriction of this property, stating that every pp-definable relation is definable by a pp-formula of polynomial length. We conjecture that the existence of such short definitions is actually equivalent to Γ having few subpowers, and verify this conjecture for a large subclass that, in particular, includes all constraint languages on three-element domains. We furthermore discuss how our conjecture imposes an upper complexity bound of co-NP on the subpower membership problem of algebras with few subpowers.

Název v anglickém jazyce

Short Definitions in Constraint Languages

Popis výsledku anglicky

A first-order formula is called primitive positive (pp) if it only admits the use of existential quantifiers and conjunction. Pp-formulas are a central concept in (fixed-template) constraint satisfaction since CSP(Γ) can be viewed as the problem of deciding the primitive positive theory of Γ, and pp-definability captures gadget reductions between CSPs. An important class of tractable constraint languages Γ is characterized by having few subpowers, that is, the number of n-ary relations pp-definable from Γ is bounded by 2^p(n) for some polynomial p(n). In this paper we study a restriction of this property, stating that every pp-definable relation is definable by a pp-formula of polynomial length. We conjecture that the existence of such short definitions is actually equivalent to Γ having few subpowers, and verify this conjecture for a large subclass that, in particular, includes all constraint languages on three-element domains. We furthermore discuss how our conjecture imposes an upper complexity bound of co-NP on the subpower membership problem of algebras with few subpowers.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/LTAUSA19070" target="_blank" >LTAUSA19070: Komutátory, kvazigrupy a Yang-Baxterova rovnice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

ISBN

978-3-95977-292-1

ISSN

—

e-ISSN

—

Počet stran výsledku

14

Strana od-do

2-15

Název nakladatele

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Místo vydání

Leibniz

Místo konání akce

Bordeaux

Datum konání akce

28. 8. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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