The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
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STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The complexity of propositional linear temporal logics in simple cases
Information and Computation
Relating linear and branching model checking
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CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
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The stuttering principle revisited
Acta Informatica
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Theoretical Computer Science - Abstract state machines and high-level system design and analysis
A parametric analysis of the state-explosion problem in model checking
Journal of Computer and System Sciences
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ACM Transactions on Computational Logic (TOCL)
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Electronic Notes in Theoretical Computer Science (ENTCS)
LTL Path Checking Is Efficiently Parallelizable
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Information Processing Letters
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IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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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.