2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128256We prove an n-EXPTIME lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n. This bound matches the known upper bound for parity games on HPDA. As a consequence the mu-calculus model checking over graphs given by n-HPDA is n-EXPTIME complete.Computer Science and Game Theorytext