An expressiveness hierarchy of Behavior Trees and related architectures

TL;DR

This paper establishes a formal hierarchy comparing the expressive power of Behavior Trees with other control architectures like decision trees and finite state machines, highlighting trade-offs in design choices.

Contribution

It introduces a formal framework for analyzing the expressiveness of control architectures and classifies Behavior Trees within this hierarchy, revealing design trade-offs.

Findings

Behavior Trees are formally compared to other architectures.

A hierarchy of control architectures based on expressiveness is proposed.

Trade-offs between readability and expressiveness in BT design are identified.

Abstract

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.