Checking Thorough Refinement on Modal Transition Systems Is EXPTIME-Complete

  • Nikola Beneš
  • Jan Křetínský
  • Kim G. Larsen
  • Jiří Srba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5684)


Modal transition systems (MTS), a specification formalism introduced more than 20 years ago, has recently received a considerable attention in several different areas. Many of the fundamental questions related to MTSs have already been answered. However, the problem of the exact computational complexity of thorough refinement checking between two finite MTSs remained unsolved.

We settle down this question by showing EXPTIME-completeness of thorough refinement checking on finite MTSs. The upper-bound result relies on a novel algorithm running in single exponential time providing a direct goal-oriented way to decide thorough refinement. If the right-hand side MTS is moreover deterministic, or has a fixed size, the running time of the algorithm becomes polynomial. The lower-bound proof is achieved by reduction from the acceptance problem of alternating linear bounded automata and the problem remains EXPTIME-hard even if the left-hand side MTS is fixed.


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nikola Beneš
    • 1
  • Jan Křetínský
    • 1
  • Kim G. Larsen
    • 2
  • Jiří Srba
    • 2
  1. 1.Faculty of InformaticsMasaryk Univ.BrnoCzech Republic
  2. 2.Department of Computer ScienceAalborg Univ.Aalborg EastDenmark

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