Sensitive Instances of the Constraint Satisfaction Problem

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421069" target="_blank" >RIV/00216208:11320/20:10421069 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.ICALP.2020.110" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2020.110</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.110" target="_blank" >10.4230/LIPIcs.ICALP.2020.110</a>

Result language

angličtina

Original language name

Sensitive Instances of the Constraint Satisfaction Problem

Original language description

We investigate the impact of modifying the constraining relations of a Constraint Satisfaction Problem (CSP) instance, with a fixed template, on the set of solutions of the instance. More precisely we investigate sensitive instances: an instance of the CSP is called sensitive, if removing any tuple from any constraining relation invalidates some solution of the instance. Equivalently, one could require that every tuple from any one of its constraints extends to a solution of the instance. Clearly, any non-trivial template has instances which are not sensitive. Therefore we follow the direction proposed (in the context of strict width) by Feder and Vardi in [13] and require that only the instances produced by a local consistency checking algorithm are sensitive. In the language of the algebraic approach to the CSP we show that a finite idempotent algebra A has a k + 2 variable near unanimity term operation if and only if any instance that results from running the (k, k + 1)-consistency algorithm on an instance over A2 is sensitive. A version of our result, without idempotency but with the sensitivity condition holding in a variety of algebras, settles a question posed by G. Bergman about systems of projections of algebras that arise from some subalgebra of a finite product of algebras. Our results hold for infinite (albeit in the case of A idempotent) algebras as well and exhibit a surprising similarity to the strict width k condition proposed by Feder and Vardi. Both conditions can be characterized by the existence of a near unanimity operation, but the arities of the operations differ by 1.

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

10101 - Pure mathematics

Project

<a href="/en/project/GA18-20123S" target="_blank" >GA18-20123S: Expanding the Scope of Universal Algebra</a><br>

Continuities

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

Publication year

2020

Confidentiality

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

Article name in the collection

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-138-2

ISSN

1868-8969

e-ISSN

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Number of pages

18

Pages from-to

1-18

Publisher name

Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany

Place of publication

Německo

Event location

Sarbrücken, Německo

Event date

Jul 8, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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