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 true antomaton (APT) acceptance problem) of possibly-infinite ranked trees generated by order-a recursion schemes is n-EXPTIME complete. We consider two subclasses of APT and investigate the complexity of the respective acceptance problems. The main results are that, for A 1:97 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 work showing that the resource usage verification for functional programs can be reduced to the model checking of recursion schemes. As an application: we show that the resource usage verification problem is (n - 1)-EXPTIME complete.