Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Strategy Construction for Parity Games with Imperfect Information
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
Directed graphs of entanglement two
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
| Hi-index | 0.00 |
We address the strategy problem for parity games with partial information and observable colors, played on finite graphs of bounded graph 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 classes 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 the partial information is unbounded we prove that the construction does not preserve boundedness of 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) tree-width, does preserve boundedness of directed path-width. Therefore, parity games with bounded partial information, played on graphs with bounded directed path-width can be solved in polynomial time.