License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.116
URN: urn:nbn:de:0030-drops-181680
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18168/
Go to the corresponding LIPIcs Volume Portal

Bodirsky, Manuel ; Knäuer, Simon

Network Satisfaction Problems Solved by k-Consistency

pdf-format:
LIPIcs-ICALP-2023-116.pdf (0.8 MB)

Abstract

We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some k ∈ ℕ, is undecidable. For the important class of finite relation algebras A with a normal representation, however, the decidability of this problem remains open. We show that if A is symmetric and has a flexible atom, then the question whether NSP(A) can be solved by k-consistency, for some k ∈ ℕ, is decidable (even in polynomial time in the number of atoms of A). This result follows from a more general sufficient condition for the correctness of the k-consistency procedure for finite symmetric relation algebras. In our proof we make use of a result of Alexandr Kazda about finite binary conservative structures.

BibTeX - Entry

@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2023.116,
  author =	{Bodirsky, Manuel and Kn\"{a}uer, Simon},
  title =	{{Network Satisfaction Problems Solved by k-Consistency}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{116:1--116:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18168},
  URN =		{urn:nbn:de:0030-drops-181680},
  doi =		{10.4230/LIPIcs.ICALP.2023.116},
  annote =	{Keywords: Constraint Satisfaction, Computational Complexity, Relation Algebras, Network Satisfaction, Qualitative Reasoning, k-Consistency, Datalog}
}

Keywords: Constraint Satisfaction, Computational Complexity, Relation Algebras, Network Satisfaction, Qualitative Reasoning, k-Consistency, Datalog
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI