Abstract: There are compelling and long-established connections between automata theory and model theory, and this talk will explore some of those connections for expansions of the real additive group. Büchi automata are the natural extension of DFAs and NFAs to a model of computation that accepts infinite-length inputs. We say a subset X of the reals is Büchi-automatic if there some natural number r and some Büchi automaton that accepts (one of) the base-r representations of every element of X, and rejects the base-r representations of each element in its complement. We can analogously define Büchi-automatic subsets of higher arities, and these sets exhibit intriguing behavior from the perspectives of both fractal geometry and model theory. In this talk, we will have the opportunity to discuss how expansions of the reals solely by Büchi-automatic sets fit into the framework of tame geometry, as well as connections to notions from metric geometry and neostability.