Automata Games for Multiple-model Checking

  • Authors:

  • Altaf Hussain;Michael Huth

  • Affiliations:

  • Department of Computing, South Kensington campus, Imperial College London, London, SW7 2AZ, United Kingdom;Department of Computing, South Kensington campus, Imperial College London, London, SW7 2AZ, United Kingdom

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2006

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Abstract

3-valued models have been advocated as a means of system abstraction such that verifications and refutations of temporal-logic properties transfer from abstract models to the systems they represent. Some application domains, however, require multiple models of a concrete or virtual system. We build the mathematical foundations for 3-valued property verification and refutation applied to sets of common concretizations of finitely many models. We show that validity checking for the modal mu-calculus has the same cost (EXPTIME-complete) on such sets as on all 2-valued models, provide an efficient algorithm for checking whether common concretizations exist for a fixed number of models, and propose using parity games on variants of tree automata to efficiently approximate validity checks of multiple models. We prove that the universal topological model in [M. Huth, R. Jagadeesan, and D. A. Schmidt. A domain equation for refinement of partial systems. Mathematical Structures in Computer Science, 14(4):469-505, 5 August 2004] is not bounded complete. This confirms that the approximations aforementioned are reasonably precise only for tree-automata-like models, unless all models are assumed to be deterministic.