On modal refinement and consistency

  • Authors:
  • Kim G. Larsen;Ulrik Nyman;Andrzej Wasowski

  • Affiliations:
  • Department of Computer Science, Aalborg University, Denmark;Department of Computer Science, Aalborg University, Denmark;Department of Computer Science, Aalborg University, Denmark

  • Venue:
  • CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
  • Year:
  • 2007

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Abstract

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 counterexmnple due to Huttel. 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) ibr modal specifications. We characterize each operationally, giving algorithms for deciding, and for synthesizing implementations, together with their complexities.