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
Graded alternating-time temporal logic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
ACM Transactions on Computational Logic (TOCL)
Branching-time logics with path relativisation
Journal of Computer and System Sciences
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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 mu-calculus, which have provided succinctness, without affecting the satisfiability of the extended logic, i.e., 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 paper, 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. This result is obtained by exploiting an automata-theoretic approach. In particular, we introduce the class of partitioning alternating Büchi tree automata and show that the emptiness problem for them is ExpTime-Complete. The satisfiability result turns even more interesting as we show that GCTL is exponentially more succinct than graded mu-calculus.