Improved model checking of hierarchical systems

Benjamin Aminof, Orna Kupferman, Aniello Murano*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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 S and a branching-time specification ψ for it, we reduce the model-checking problem (does S satisfy ψ?) to the problem of solving a hierarchical game obtained by taking the product of S with an alternating tree automaton 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.

Original languageAmerican English
Pages (from-to)68-86
Number of pages19
JournalInformation and Computation
StatePublished - Jan 2012

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: (B. Aminof), (O. Kupferman), (A. Murano). 1 This work was partially done while the author was visiting Università degli Studi di Napoli “Federico II”, supported by ESF GAMES project, short visit grant n.2789. 2 Partially supported by ESF GAMES project, Vigevani Project Prize 2010–2011, and by University of Napoli Federico II under the F.A.R.O. project.


  • Abstraction-refinement
  • Branching-time temporal logics
  • Hierarchical systems
  • Model checking
  • Parity games
  • Two-player games


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