Finite Automata Encoding Functions

Finite automata are used to describe functions, geometric figures, fractals and as a tool for image compression. We introduce a new family of functions $f: \mathbb{R}^d \rightarrow \mathbb{R}$ encoded as finite automata by utilizing hierarchical tensor product B-splines and the theory of FA-presentable structures. We show that some problems which appear in the framework of hierarchical tensor product B-splines can be efficiently solved using the introduced encoding.