Model checking restricted sets of timed paths

  • Authors:
  • Nicolas Markey;Jean-François Raskin

  • Affiliations:
  • Lab. Spécification et Vérification, ENS Cachan, Cachan Cedex, France;Département d'Informatique, Université Libre de Bruxelles, Brussels, Belgium

  • Venue:
  • Theoretical Computer Science - Concurrency theory (CONCUR 2004)
  • Year:
  • 2006

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Abstract

In this paper, we study the complexity of model-checking formulas of four important real-time logics (TPTL, MTL, MITL, and TCTL) over restricted sets of timed paths. The classes of restricted sets of timed paths that we consider are (i) a single finite (or ultimately periodic) timed path, (ii) an infinite set of finite (or infinite) timed paths defined by a finite (or ultimately periodic) path in a region graph, (iii) an infinite set of finite (or infinite) timed paths defined by a finite (or ultimately periodic) path in a zone graph.Several results are quite negative: TPTL and MTL remain undecidable along region-and zone-paths. On the other hand, we obtained PTIME algorithms for model-checking TCTL along a region path, and for MTL along a single timed path.