Parity Games with Partial Information Played on Graphs of Bounded Complexity [chapter]

Bernd Puchala, Roman Rabinovich
2010 Lecture Notes in Computer Science  
We address the strategy problem for parity games with partial information and observable colors, played on finite graphs of bounded complexity. We consider several measures for the complexity of graphs and analyze in which cases, bounding the measure decreases the complexity of the strategy problem on the corresponding class of graphs. We prove or disprove that the usual powerset construction for eliminating partial information preserves boundedness of the graph complexity. For the case where
more » ... e partial information is unbounded we prove that this is not the case for any measure we consider. We also prove that the strategy problem is Exptime-hard on graphs with directed path-width at most 2 and Pspace-complete on acyclic graphs. For games with bounded partial information we obtain that the powerset construction, while neither preserving boundedness of entanglement nor of (undirected) treewidth, does preserve boundedness of directed path-width. Hence, parity games with bounded partial information, played on graphs with bounded directed path-width can be solved in polynomial time.
doi:10.1007/978-3-642-15155-2_53 fatcat:tqi43uqoxzhejeddkdy2bfsaya