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Computation tree logic with deadlock detection

Authors

Rob van Glabbeek, Bas Luttik and Nikola Trčka

NICTA

UNSW

Eindhoven University of Technology

CWI

Abstract

We study the equivalence relation on states of labelled transition systems of satisfying the same formulas in Computation Tree Logic without the next state modality (CTL-X). This relation is obtained by De Nicola & Vaandrager by translating labelled transition systems to Kripke structures, while lifting the totality restriction on the latter. They characterised it as divergence sensitive branching bisimulation equivalence.

We find that this equivalence fails to be a congruence for interleaving parallel composition. The reason is that the proposed application of CTL-X to non-total Kripke structures lacks the expressiveness to cope with deadlock properties that are important in the context of parallel composition. We propose an extension of CTL-X, or an alternative treatment of non-totality, that fills this hiatus. The equivalence induced by our extension is characterised as branching bisimulation equivalence with explicit divergence, which is, moreover, shown to be the coarsest congruence contained in divergence sensitive branching bisimulation equivalence.

BibTeX Entry

  @article{vanGlabbeek_LT_09,
    author           = {van Glabbeek, Robert and Luttik, Bas and Trčka, Nikola},
    journal          = {Logical Methods in Computer Science},
    issn             = {1860-5974},
    number           = {4:5},
    month            = dec,
    volume           = {5},
    year             = {2009},
    keywords         = {concurrency, temporal logic, kripke structures, labelled transition systems, stuttering equivalence,
                        branching bisimulation, divergence, deadlock.},
    title            = {Computation Tree Logic with Deadlock Detection},
    pages            = {1-24}
  }

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