Improved Model Checking of Hierarchical Systems

  • Benjamin Aminof
  • Orna Kupferman
  • Aniello Murano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5944)


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.


Model Check Hierarchical System Winning Strategy Exit Node Summary Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Benjamin Aminof
    • 1
  • Orna Kupferman
    • 1
  • Aniello Murano
    • 2
  1. 1.Hebrew UniversityJerusalemIsrael
  2. 2.Università degli Studi di Napoli “Federico II”NapoliItaly

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