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.

混合分叉时间逻辑是支化时间逻辑等CTL，CTL的强大的扩展^⁎或甚至模态μ演算通过加入粘合剂，跳跃和可变测试。它们的表现力不再受双仿真不变性的限制。因此，它们不保留树模型属性，并且有限模型属性同样丢失。它们的可满足性问题通常是无法确定的，其模型检查问题（在有限模型上）可以从多项式到非基本时间确定。

在本文中，我们研究了这种混合分支时间逻辑的表达能力。我们分支时间逻辑CTL，CTL的层次扩展⁺，CTL ^⁎和模态μ演算到他们的混合扩展。我们表明，即使所需的技术越来越复杂，大多数分离结果也可以转移到混合世界。我们还给出了线性，树形和有限模型的倒塌结果。