Bisimulation invariant monadic-second order logic in the finite.

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 Image 1 coincides with L μ. [ABSTRACT FROM AUTHOR]