Complexity of decision problems for mixed and modal specifications

  • Authors:
  • Adam Antonik;Michael Huth;Kim G. Larsen;Ulrik Nyman;Andrzej Wąsowski

  • Affiliations:
  • Department of Computing, Imperial College London, United Kingdom;Department of Computing, Imperial College London, United Kingdom;Department of Computer Science, Aalborg University, Denmark;Department of Computer Science, Aalborg University, Denmark;Department of Computer Science, Aalborg University, Denmark and IT University of Copenhagen, Denmark

  • Venue:
  • FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
  • Year:
  • 2008

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Abstract

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 PSPACEhard for mixed, while trivial for modal specifications. We also supply upper bounds suggesting strong links between these problems.