BTL2 and the expressive power of ECTL+

Alexander Rabinovich, Philippe Schnoebelen

Research output: Contribution to journalArticlepeer-review


We show that ECTL+, the classical extension of CTL with fairness properties, is expressively equivalent to BTL2, a natural fragment of the monadic logic of order. BTL2 is the branching-time logic with arbitrary quantification over paths, and where path formulae are restricted to quantifier depth 2 first-order formulae in the monadic logic of order. This result, linking ECTL+ to a natural fragment of the monadic logic of order, provides a characterization that other branching-time logics, e.g., CTL, lack. We then go on to show that ECTL+ and BTL2 are not finitely based (i.e., they cannot be defined by a finite set of temporal modalities) and that their model-checking problems are of the same complexity.

Original languageEnglish
Pages (from-to)1023-1044
Number of pages22
JournalInformation and Computation
Issue number7
StatePublished - Jul 2006


  • Expressivity of branching-time temporal logic
  • Model checking


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