Complexity and Succinctness Issues for Linear-Time Hybrid Logics

  • Laura Bozzelli
  • Ruggero Lanotte
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5293)


Full linear-time hybrid logic (HL) is a non-elementary and equally expressive extension of standard LTL + past obtained by adding the well-known binder operators ↓ and ∃. We investigate complexity and succinctness issues for HL in terms of the number of variables and nesting depth of binder modalities. First, we present direct automata-theoretic decision procedures for satisfiability and model-checking of HL, which require space of exponential height equal to the nesting depth of binder modalities. The proposed algorithms are proved to be asymptotically optimal by providing matching lower bounds. Second, we show that for the one-variable fragment of HL, the considered problems are elementary and, precisely, Expspace-complete. Finally, we show that for all 0 ≤ h < k, there is a succinctness gap between the fragments HL k and HL h with binder nesting depth at most k and h, respectively, of exponential height equal to k − h.


Model Check Binder Modality Acceptance Condition Kripke Structure Hybrid Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Laura Bozzelli
    • 1
  • Ruggero Lanotte
    • 1
  1. 1.Università dell’InsubriaComoItaly

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