The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom

Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify computational complexity of network satisfaction problem for all finite relation algebras A. We provide a complete classification case that A is symmetric and has fexible atom; this case, NP-complete or P. The task can be reduced to where integral. If integral algebra flexible atom, then it normal representation B. study using universal-algebraic approach, via an analysis polymorphisms also use Ramsey-type result Nešetřil Rödl dichotomy Bulatov conservative finite-domain constraint problems.