Short Definitions in Constraint Languages

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Short Definitions in Constraint Languages

Original language description

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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

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

Project

<a href="/en/project/LTAUSA19070" target="_blank" >LTAUSA19070: Commutators, quasigroups and Yang Baxter equation</a><br>

Continuities

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

Publication year

2023

Confidentiality

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

Article name in the collection

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

ISBN

978-3-95977-292-1

ISSN

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e-ISSN

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Number of pages

14

Pages from-to

2-15

Publisher name

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Place of publication

Leibniz

Event location

Bordeaux

Event date

Aug 28, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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