An Improved Recursive Algorithm for Parity Games

An improved recursive algorithm is presented in this paper for reducing the number of recursive calls in parity games. The improvement is two-fold: (1) A pre-processing algorithm is presented first to seek out and remove atomic winning regions which probably result in exponentially many recursive calls from a game graph, (2) a conditional statement is inserted before the second recursive call of the existing algorithm where in case the condition is satisfied, the result can be obtained directly without executing the second recursive call.