Abstract
Hybrid branching-time logics are a powerful extension of branching-time logics like CTL, CTL⁎ or even the modal μ-calculus through the addition of binders, jumps and variable tests. Their expressiveness is not restricted by bisimulation-invariance anymore. Hence, they do not retain the tree model property, and the finite model property is equally lost. Their satisfiability problems are typically undecidable, their model checking problems (on finite models) are decidable with complexities ranging from polynomial to non-elementary time.In this paper we study the expressive power of such hybrid branching-time logics. We extend the hierarchy of branching-time logics CTL, CTL+, CTL⁎ and the modal μ-calculus to their hybrid extensions. We show that most separation results can be transferred to the hybrid world, even though the required techniques become more involved. We also present collapse results for linear, tree-shaped and finite models.
Highlights
Temporal logics like LTL [14], CTL [7] and CTL∗ [9] are important specification formalisms for the behaviour of programs because they extend modal logic with the ability to reason about properties of unbounded or infinite computations
We can consider hybrid variants of weaker branching-time temporal logics as they are known in the literature: if we restrict the temporal operators further to not allow nesting of path formulas with the exception of fairness constraints, i.e. path formulas are generated by the grammar ψ := φ | ¬ψ | ψ ∨ ψ | Xφ | φUφ | GFφ we obtain the logic HFCTL+
We have studied the expressive power of hybrid branching-time logics
Summary
Temporal logics like LTL [14], CTL [7] and CTL∗ [9] are important specification formalisms for the behaviour of programs because they extend modal logic with the ability to reason about properties of unbounded or infinite computations Their satisfiability and model checking problems are decidable, ranging from polynomial [7] to doubly exponential time [10]. The paper at hand presents some first results on a study of the expressive power of hybrid logics that results from an extension of well-known branching-time temporal logics – mostly CTL∗ and its fragments like CTL and CTL+– with the aforementioned first-order features.
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