Improved model checking of hierarchical systems

  • Authors:

  • Benjamin Aminof;Orna Kupferman;Aniello Murano

  • Affiliations:

  • Hebrew University, School of Eng. and Computer Science, Jerusalem 91904, Israel;Hebrew University, School of Eng. and Computer Science, Jerusalem 91904, Israel;Universití degli Studi di Napoli "Federico II", 80126 Napoli, Italy

  • Venue:
  • Information and Computation
  • Year:
  • 2012

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