  In this paper we provide a formal framework for comparing the expressive
power of Behavior Trees (BTs) to other action selection architectures. Taking
inspiration from the analogous comparisons of structural programming
methodologies, we formalise the concept of `expressiveness'. This leads us to
an expressiveness hierarchy of control architectures, which includes BTs,
Decision Trees (DTs), Teleo-reactive Programs (TRs) and Finite State Machines
(FSMs). By distinguishing between BTs with auxiliary variables and those
without, we demonstrate the existence of a trade-off in BT design between
readability and expressiveness. We discuss what this means for BTs in practice.
