### Faculty Member

### Project Image

In the last few years novel connections between mathematical logic, automata theory and metric geometry have emerged. A question that often arises in this area is the following: if *r*ise a natural number greater than one, and *C* is a geometrically interesting subset of **R*** ^{n}*, can the set of all

*r*-ary representations of elements of

*C*be recognized by a Büchi automaton? For example, let

*C*be the usual middle-thirds Cantor set. Elements of

*C*are precisely those real numbers in

*[0,1]*that have a ternary representation in which the digit

*1*does not occur. Therefore it is not hard to see that the set of ternary representations of elements of

*C*can be recognized by such an automaton. The goal of this project to answer similar questions in the case that

*C*is the graph of a function. In particular, we want know whether there is a non-affine, differentiable function whose graph can be recognized in this way. This is a continuation of the project "Automata and space-filling curves" from the Fall semester 2017.

### Team Meetings

### Project Difficulty

### Undergrad Prerequisites

Basic knowledge of automata required, and participants should have completed a proof-based course in real analysis.