This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations of Boolean and arithmetic operations allowed in constraints, one obtains several distinct logics generalizing CTL. We provide a thorough analysis of their expressiveness and of the complexity of their model-checking problem (ranging from P-complete to undecidable).


Model Check Temporal Logic Atomic Proposition Kripke Structure Boolean Combination 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • François Laroussinie
    • 1
  • Antoine Meyer
    • 2
  • Eudes Petonnet
    • 1
  1. 1.LIAFAUniversité Paris Diderot – Paris 7 & CNRS UMRFrance
  2. 2.LIGMUniversité Paris Est – Marne-la-Valle & CNRS UMRFrance

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