The Complexity of Model Checking (Collapsible) Higher-Order Pushdown Systems

We study (collapsible) higher-order pushdown systems --- theoretically robust and well-studied models of higher-order programs --- along with their natural subclass called (collapsible) higher-order basic process algebras. We provide a comprehensive analysis of the model checking complexity of a range of both branching-time and linear-time temporal logics. We obtain tight bounds on data, expression, and combined-complexity for both (collapsible) higher-order pushdown systems and (collapsible) higher-order basic process algebra. At order-$k$, results range from polynomial to $(k+1)$-exponential time. Finally, we study (collapsible) higher-order basic process algebras as graph generators and show that they are almost as powerful as (collapsible) higher-order pushdown systems up to MSO interpretations