Complexity of Model Checking Recursion Schemes for Fragments of the Modal Mu-Calculus

Ong has shown that the modal mu-calculus model checking problem(equivalently, the alternating parity tree automaton (APT) acceptance problem)of possibly-infinite ranked trees generated by order-n recursion schemes isn-EXPTIME complete. We consider two subclasses of APT and investigate thecomplexity of the respective acceptance problems. The main results are that,for APT with a single priority, the problem is still n-EXPTIME complete;whereas, for APT with a disjunctive transition function, the problem is(n-1)-EXPTIME complete. This study was motivated by Kobayashi's recent workshowing that the resource usage verification of functional programs can bereduced to the model checking of recursion schemes. As an application, we showthat the resource usage verification problem is (n-1)-EXPTIME complete