The power of reachability testing for timed automata

  • Authors:
  • Luca Aceto;Patricia Bouyer;Augusto Burgueño;Kim G. Larsen

  • Affiliations:
  • BRICS (Basic Research in Computer Science), Department of Computer Science, Aalborg University, Fredrik Bajers Vej 7-E, DK-9220 Aalborg Ø, Denmark;Laboratoire Spécification et Vérification, CNRS UMR 8643, Ecole Normale Supérieure de Cachan, 61, avenue du Président Wilson, F-94235 Cachan Cedex, France;European Commission, Research Directorate-General, Rue de la Loi 200, B-1049 Brussels, Belgium;BRICS (Basic Research in Computer Science), Department of Computer Science, Aalborg University, Fredrik Bajers Vej 7-E, DK-9220 Aalborg Ø, Denmark

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

The computational engine of the verification tool UPPALL consists of a collection of efficient algorithms for the analysis of teachability properties of systems. Model-checking of properties other than plain reachability ones may currently be carried out in such a tool as follows. Given a property φ to model-check, the user must provide a test automaton Tφ for it. This test automaton must be such that the original system S has the property expressed by φ precisely when none of the distinguished reject states of Tφ can be reached in the synchronized parallel composition of S with Tφ. This raises the question of which properties may be analysed by UPPAAL in such a way. This paper gives an answer to this question by providing a complete characterization of the class of properties for which model-checking can be reduced to reachability testing in the sense outlined above. This result is obtained as a corollary of a stronger statement pertaining to the compositionality of the property language considered in this study. In particular, it is shown that our language is the least expressive compositional language that can express a simple safety property stating that no reject state can ever be reached.Finally, the property language characterizing the power of reachability testing is used to provide a definition of characteristics properties with respect to a timed version of the ready simulation preorder, for nodes of τ-free, deterministic timed automata.