The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
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Theories of computability
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On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The complexity of propositional linear temporal logics in simple cases
Information and Computation
A game-based verification of non-repudiation and fair exchange protocols
Journal of Computer Security - IFIP 2000
Optimal satisfiability for propositional calculi and constraint satisfaction problems
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Acta Informatica
Infinite State AMC-Model Checking for Cryptographic Protocols
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
From Philosophical to Industrial Logics
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
The Tractability of Model-checking for LTL: The Good, the Bad, and the Ugly Fragments
Electronic Notes in Theoretical Computer Science (ENTCS)
Model Checking CTL is Almost Always Inherently Sequential
TIME '09 Proceedings of the 2009 16th International Symposium on Temporal Representation and Reasoning
The complexity of generalized satisfiability for linear temporal logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Computationally sound analysis of a probabilistic contract signing protocol
ESORICS'09 Proceedings of the 14th European conference on Research in computer security
Generalized modal satisfiability
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Temporal logic for process specification and recognition
Intelligent Service Robotics
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In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If in contrast, the set of propositional operators is restricted, the complexity may decrease. This article systematically studies the model-checking problem for LTL formulae over restricted sets of propositional and temporal operators. For almost all combinations of temporal and propositional operators, we determine whether the model-checking problem is tractable (in PTIME) or intractable (NP-hard). We then focus on the tractable cases, showing that they all are NL-complete or even logspace solvable. This leads to a surprising gap in complexity between tractable and intractable cases. It is worth noting that our analysis covers an infinite set of problems, since there are infinitely many sets of propositional operators.