Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree

  • Thilo Hafer
  • Wolfgang Thomas
Temporal Logic, Concurrent Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


In this paper we study the expressive power of the full branching time logic CTL* (of Clarke, Emerson, Halpern and Sistla), by comparing it with fragments of monadic second-order logic over the binary tree. We show that over binary tree models the system CTL* has the same expressive power as monadic second-order logic in which set quantification is restricted to infinite paths (in particular, the full strength of first-order logic is captured here by CTL*). This generalizes Kamp's theorem on the equivalence between propositional linear time logic and first-order logic over the ordering of the natural numbers. For the proof an extension of CTL* by past operators is introduced. The transition from monadic formulas to CTL* rests on a model-theoretic decomposition lemma for trees that is justified by an application of the Ehrenfeucht-Fraissé game. The paper concludes by discussing variants of the main result, dealing for example with trees of higher branching index and the extended branching time logic ECTL*.


Binary Tree Kripke Structure Tree Language Computation Tree Logic Linear Time Temporal Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Thilo Hafer
    • 1
  • Wolfgang Thomas
    • 1
  1. 1.Lehrstuhl für Informatik IIRWTH AachenAachenWest-Germany

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