Game semantics of higher-order recursion schemes establishes the decidability ofMSO model-checking

This article presents two different ways of model-checking higher-order recursion schemes, both relying on game semantics. A given recursion scheme is translated to another, which is its computational extent, in the sense that β-reduction paths called traversals in the new generated tree are isomorphic to branches of the former tree. Then, the two approaches differ on their way of simulating traversals: one uses APTs to produce verification parity games, whereas the other uses n-CPDAs and builds verification parity games on their transition graphs. Both approaches prove that the modal μ-calculus model-checking of an order-n recursion scheme is n-EXPTIME complete.