On Modal Refinement and Consistency

  • Kim G. Larsen
  • Ulrik Nyman
  • Andrzej Wąsowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4703)


Almost 20 years after the original conception, we revisit several fundamental question about modal transition systems. First, we demonstrate the incompleteness of the standard modal refinement using a counterexample due to Hüttel. Deciding any refinement, complete with respect to the standard notions of implementation, is shown to be computationally hard (co-NP hard). Second, we consider four forms of consistency (existence of implementations) for modal specifications. We characterize each operationally, giving algorithms for deciding, and for synthesizing implementations, together with their complexities.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kim G. Larsen
    • 1
  • Ulrik Nyman
    • 1
  • Andrzej Wąsowski
    • 1
  1. 1.Department of Computer Science, Aalborg UniversityDenmark

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