TY - JOUR
AU - Bodirsky, Manuel
AU - Knäuer, Simon
PY - 2021/05/18
Y2 - 2024/02/22
TI - Network Satisfaction for Symmetric Relation Algebras with a Flexible Atom
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 35
IS - 7
SE - AAAI Technical Track on Knowledge Representation and Reasoning
DO - 10.1609/aaai.v35i7.16773
UR - https://ojs.aaai.org/index.php/AAAI/article/view/16773
SP - 6218-6226
AB - Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is symmetric and has a flexible atom; the problem is in this case NP-complete or in P. If a finite integral relation algebra has a flexible atom, then it has a normal representation B. We can then study the computational complexity of the network satisfaction problem of A using the universal-algebraic approach, via an analysis of the polymorphisms of B. We also use a Ramsey-type result of Nešetřil and Rödl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.
ER -