Positional Strategies for Higher-Order Pushdown Parity Games

Abstract

Higher-order pushdown systems generalize pushdown systems by using higher-order stacks, which are nested stacks of stacks. In this article, we consider parity games defined by higher-order pushdown systems and provide a k-Exptime algorithm to compute finite representations of positional winning strategies for both players for games defined by level-k higher-order pushdown automata. Our result is based on automata theoretic techniques exploiting the tree structure corresponding to higher-order stacks and their associated operations.