Infinite Games over Higher-Order Pushdown Systems

In this thesis we deal with games over infinite graphs with regular winning conditions. A well studied family of such games are the pushdown games. An important result for these games is that the winning region can be described by regular sets of configurations. We extend this result to games defined by higher-order pushdown systems. The higher-order pushdown systems extend the usual pushdown systems by the use of higher-order stacks which are stacks of stacks of stacks etc.. We concentrate in this thesis just on level 2 stacks that are stacks that contain a sequence of level 1 stacks but the results can easily be lifted to level n. The operations to manipulate those stacks are the simple level 1 operations push and pop and also operations that can copy and destroy the topmost level 1 stacks inside the level 2 stack. For the definition of regularity over higher-order pushdown stacks we use a technique recently developed by Carayol in [Car05]. We will present an algorithm to compute the winning regions of reachability and parity games over higher-order pushdown graphs.