“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree
14th International Colloquium on Automata, languages and programming
Handbook of theoretical computer science (vol. B)
Automated temporal reasoning about reactive systems
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Modalities for model checking (extended abstract): branching time strikes back
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Communication and Concurrency
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
"Sometime" is sometimes "not never": on the temporal logic of programs
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the First International Conference on Temporal Logic
ICTL '94 Proceedings of the First International Conference on Temporal Logic
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
On the Expressive Power of CTL
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Decision procedures and expressiveness in the temporal logic of branching time
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
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Many temporal logics were suggested as branching time specification formalisms during the last 20 years. These logics were compared against each other for their expressive power, model checking complexity and succinctness. Yet, unlike the case for linear time logics, no canonical temporal logic of branching time was agreed upon. We offer an explanation for the multiplicity of temporal logics over branching time and provide an objective quantified 'yardstick' to measure these logics. We define an infinite hierarchy BTLk of temporal logics and prove its strictness. We show that CTL* has no finite base, and that almost all of its many sub-logics suggested in the literature are inside the second level of our hierarchy. We show that for every logic based on a finite set of modalities, the complexity of model checking is linear both in the size of structure and the size of formula.