Abstract
Monadic second-order logic (MSOL) provides a general framework for expressing properties of reactive systems as modelled by trees. Monadic path logic (MPL) is obtained by restricting second-order quantification to paths reflecting computation sequences. In this paper we show that the expressive power of MPL over trees coincides with the usual branching time logic CTL* embellished with a simple form of counting. As a corollary, we derive an earlier result that CTL* coincides with the bisimulation-invariant properties of MPL. In order to prove the main result, we first prove a new Composition Theorem for trees.
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