Abstract: Linear genetic programming (LGP) is a genetic programming paradigm based on a linear sequence of operations being executed. An LGP individual can be decoded into a directed acyclic graph (DAG). In particular, we will focus on its application in numerical approximations of mathematical functions. Computers calculate transcendental functions by approximating them through the composition of a few limited
precision instructions. I will first review some of the recent progress in graph-based linear genetic programming, including "AutoNumerics-Zero," recently developed by Google DeepMind. Then, I will introduce the mathematical structure of DAGs under the context and discuss the complexity of the function space corresponding to a DAG. Finally, I will interpret the LGP as a dynamic system and propose some open problems related to its ergodicity.