Decision procedures and expressiveness in the temporal logic of branching time
Journal of Computer and System Sciences
“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
Alternating automata on infinite trees
Theoretical Computer Science
Attributive concept descriptions with complements
Artificial Intelligence
Handbook of theoretical computer science (vol. B)
Weak alternating automata and tree automata emptiness
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
"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
CTL+ is Exponentially more Succinct than CTL
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Weak, strong, and strong cyclic planning via symbolic model checking
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
Counting on CTL: on the expressive power of monadic path logic
Information and Computation
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Temporal Logics over Unranked Trees
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Memoryful Branching-Time Logic
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Complexity and succinctness of public announcement logic
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
IEEE Transactions on Software Engineering
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
A purely model-theoretic proof of the exponential succinctness gap between CTL+ and CTL
Information Processing Letters
The On-Line Encyclopedia of Integer Sequences
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
CTL Model-Checking with Graded Quantifiers
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Reasoning about XML with Temporal Logics and Automata
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Graded-CTL: Satisfiability and Symbolic Model Checking
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Graded computation tree logic with binary coding
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Combining temporal logics for querying XML documents
ICDT'07 Proceedings of the 11th international conference on Database Theory
A decision procedure for CTL* based on tableaux and automata
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Pushdown module checking with imperfect information
Information and Computation
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In modal logics, graded (world) modalities have been deeply investigated as a useful framework for generalizing standard existential and universal modalities in such a way that they can express statements about a given number of immediately accessible worlds. These modalities have been recently investigated with respect to the μCalculus, which have provided succinctness, without affecting the satisfiability of the extended logic, that is, it remains solvable in ExpTime. A natural question that arises is how logics that allow reasoning about paths could be affected by considering graded path modalities. In this article, we investigate this question in the case of the branching-time temporal logic CTL (GCTL, for short). We prove that, although GCTL is more expressive than CTL, the satisfiability problem for GCTL remains solvable in ExpTime, even in the case that the graded numbers are coded in binary. This result is obtained by exploiting an automata-theoretic approach, which involves a model of alternating automata with satellites. The satisfiability result turns out to be even more interesting as we show that GCTL is at least exponentially more succinct than graded μCalculus.