eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-05
116:1
116:20
10.4230/LIPIcs.ICALP.2023.116
article
Network Satisfaction Problems Solved by k-Consistency
Bodirsky, Manuel
1
https://orcid.org/0000-0001-8228-3611
Knäuer, Simon
1
Institut für Algebra, TU Dresden, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol261-icalp2023/LIPIcs.ICALP.2023.116/LIPIcs.ICALP.2023.116.pdf
Constraint Satisfaction
Computational Complexity
Relation Algebras
Network Satisfaction
Qualitative Reasoning
k-Consistency
Datalog