Abstract
We present a unified game-based approach for branching-time model checking of hierarchical systems. Such systems are exponentially more succinct than standard state-transition graphs, as repeated sub-systems are described only once. Early work on model checking of hierarchical systems shows that one can do better than a naive algorithm that “flattens” the system and removes the hierarchy.
Given a hierarchical system \(\mathcal S\) and a branching-time specification ψ for it, we reduce the model-checking problem (does \(\mathcal S\) satisfy ψ?) to the problem of solving a hierarchical game obtained by taking the product of \(\mathcal S\) with an alternating tree automaton \({\mathcal A}_\psi\) for ψ. Our approach leads to clean, uniform, and improved model-checking algorithms for a variety of branching-time temporal logics. In particular, by improving the algorithm for solving hierarchical parity games, we are able to solve the model-checking problem for the μ-calculus in Pspace and time complexity that is only polynomial in the depth of the hierarchy. Our approach also leads to an abstraction-refinement paradigm for hierarchical systems. The abstraction maintains the hierarchy, and is obtained by merging both states and sub-systems into abstract states.
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Aminof, B., Kupferman, O., Murano, A. (2010). Improved Model Checking of Hierarchical Systems. In: Barthe, G., Hermenegildo, M. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2010. Lecture Notes in Computer Science, vol 5944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11319-2_8
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