2011 | OriginalPaper | Chapter
Weak Kripke Structures and LTL
Authors : Lars Kuhtz, Bernd Finkbeiner
Published in: CONCUR 2011 – Concurrency Theory
Publisher: Springer Berlin Heidelberg
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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
.