Modal and mixed specifications: Key decision problems and their complexities

  • Authors:
  • Adam Antonik;Michael Huth;Kim g. Larsen;Ulrik Nyman;Andrzej WĄ/sowski

  • Affiliations:
  • Cnrs, ecole normale supé/rieure de cachan, france email: antonik@lsv.ens-cachan.fr;Department of computing, imperial college london, united kingdom email: m.huth@imperial.ac.uk;Department of computer science, aalborg university, denmark email: kgl@cs.aau.dk/ ulrik@cs.aau.dk;Department of computer science, aalborg university, denmark email: kgl@cs.aau.dk/ ulrik@cs.aau.dk;It university of copenhagen, denmark email: wasowski@itu.dk

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2010

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Abstract

Modal and mixed transition systems are specification formalisms that allow the mixing of over-and under-approximation. We discuss three fundamental decision problems for such specifications: —whether a set of specifications has a common implementation;—whether an individual specification has an implementation; and—whether all implementations of an individual specification are implementations of another one. For each of these decision problems we investigate the worst-case computational complexity for the modal and mixed cases. We show that the first decision problem is EXPTIME-complete for both modal and mixed specifications. We prove that the second decision problem is EXPTIME-complete for mixed specifications (it is known to be trivial for modal ones). The third decision problem is also shown to be EXPTIME-complete for mixed specifications.