Weak Kripke Structures and LTL

  • Lars Kuhtz
  • Bernd Finkbeiner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)


We revisit the complexity of the model checking problem for formulas of linear-time temporal logic (LTL). We show that the classic PSPACE-hardness result is actually limited to a subclass of the Kripke frames, which is characterized by a simple structural condition: the model checking problem is only PSPACE-hard if there exists a strongly connected component with two distinct cycles. If no such component exists, the problem is in coNP. If, additionally, the model checking problem can be decomposed into a polynomial number of finite path checking problems, for example if the frame is a tree or a directed graph with constant depth, or the frame has an SCC graph of constant depth, then the complexity reduces further to NC.


Model Check Turing Machine Constant Depth Atomic Proposition Computation Path 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lars Kuhtz
    • 1
  • Bernd Finkbeiner
    • 2
  1. 1.Microsoft RedmondUSA
  2. 2.Saarland UniversityGermany

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