Complexity of Decision Problems for Mixed and Modal Specifications

  • Adam Antonik
  • Michael Huth
  • Kim G. Larsen
  • Ulrik Nyman
  • Andrzej Wąsowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4962)


We consider decision problems for modal and mixed transition systems used as specifications: the common implementation problem (whether a set of specifications has a common implementation), the consistency problem (whether a single specification has an implementation), and the thorough refinement problem (whether all implementations of one specification are also implementations of another one). Common implementation and thorough refinement are shown to be PSPACE-hard for modal, and so also for mixed, specifications. Consistency is PSPACE-hard for mixed, while trivial for modal specifications. We also supply upper bounds suggesting strong links between these problems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Adam Antonik
    • 1
  • Michael Huth
    • 1
  • Kim G. Larsen
    • 2
  • Ulrik Nyman
    • 2
  • Andrzej Wąsowski
    • 2
    • 3
  1. 1.Department of ComputingImperial College LondonUnited Kingdom
  2. 2.Department of Computer ScienceAalborg UniversityDenmark
  3. 3.IT University of CopenhagenDenmark

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