“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
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
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
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
CTL Model-Checking with Graded Quantifiers
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
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
ACM Transactions on Computational Logic (TOCL)
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Graded path quantifiers have been recently introduced and investigated as a useful framework for generalizing standard existential and universal path quantifiers in the branching-time temporal logic CTL (GCTL), in such a way that they can express statements about a minimal and conservative number of accessible paths. These quantifiers naturally extend to paths the concept of graded world modalities, which has been deeply investigated for the µ-CALCULUS (Gµ-CALCULUS) where it allows to express statements about a given number of immediately accessible worlds. As for the "non-graded" case, it has been shown that the satisfiability problem for GCTL and the Gµ-CALCULUS coincides and, in particular, it remains solvable in EXPTIME. However, GCTL has been only investigated w.r.t. graded numbers coded in unary, while Gµ-CALCULUS uses for this a binary coding, and it was left open the problem to decide whether the same result may or may not hold for binary GCTL. In this paper, by exploiting an automata theoretic-approach, which involves a model of alternating automata with satellites, we answer positively to this question. We further investigate the succinctness of binary GCTL and show that it is at least exponentially more succinct than Gµ-CALCULUS.