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

TL;DR

This paper analyzes the computational complexity of model checking recursion schemes for fragments of the modal mu-calculus, revealing how restrictions on automata influence complexity and applying results to resource usage verification.

Contribution

It identifies the complexity of model checking for specific subclasses of automata, extending Ong's results and applying them to resource verification.

Findings

Model checking with a single priority remains n-EXPTIME complete.

Disjunctive transition functions reduce complexity to (n-1)-EXPTIME.

Resource usage verification is (n-1)-EXPTIME complete.

Abstract

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 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 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 work showing that the resource usage verification of 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.