We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the modal μ-calculus. Using these characterisations we prove for some simple classes of transition systems that this is indeed the case. In particular, we show that, over the class of all finite transition systems with Cantor–Bendixson rank at most k, bisimulation-invariant

coincides with ${\mathrm{L}}_{\mu }$.

中文翻译：

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有限元中的双仿真不变二阶二阶逻辑

我们考虑了各种类型的有限转移系统上的双仿真不变式一阶二阶逻辑。我们目前几个组合表征的，当这个片段一致的表现力与模态μ演算。使用这些特征，我们证明了某些简单类型的过渡系统确实是这种情况。尤其是，我们证明，在Cantor–Bendixson秩最高为k的所有有限过渡系统的类中，双仿真不变

符合 ${\mathrm{大号}}_{\mu }$。