Complexity of model checking recursion schemes for fragments of the modal mu-calculus. (English) Zbl 1248.68334
Albers, Susanne (ed.) et al., Automata, languages and programming. 36th international colloquium, ICALP 2009, Rhodes, Greece, July 5–12, 2009. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-02929-5/pbk). Lecture Notes in Computer Science 5556, 223-234 (2009).
Summary: 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 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.
For the entire collection see [Zbl 1166.68002].
For the entire collection see [Zbl 1166.68002].
MSC:
| 68Q60 | Specification and verification (program logics, model checking, etc.) |
| 03B45 | Modal logic (including the logic of norms) |
| 68Q17 | Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) |
