EXPTIME-complete Decision Problems for Modal and Mixed 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;IT University of Copenhagen, Denmark

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

Modal and mixed transition systems are formalisms that allow mixing of over- and under-approximation in a single specification. We show EXPTIME-completeness of three fundamental decision problems for such specifications: whether a set of modal or mixed specifications has a common implementation, whether a sole mixed specification has an implementation, and whether all implementations of one mixed specification are implementations of another mixed or modal one. These results are obtained by a chain of reductions starting with the acceptance problem for linearly bounded alternating Turing machines.