Counting on CTL*: on the expressive power of monadic path logic

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. © 2003 Elsevier Science (USA). All rights reserved.