Logic Seminar

Alexi Taylor Block Gorman, University of Illinois at Urbana-Champaign

"Continuous Regular Functions: where automata theory meets metric geometry"

The results in this talk illustrate and expand on crucial connections between automata theory and metric geometry. We use the connection between Buchi automata and iterated function systems to characterize which continuous functions and which differentiable functions are recognized by a Buchi automaton.  In particular, we show that a continuous regular function (with closed and bounded domain) is affine off of a nowhere dense set with measure zero. As a result, we show that every differentiable regular function is affine. These results are joint work with Philipp Hieronymi, Erik Walsberg, Elliot Kaplan, and our team of undergraduate researchers in the Illinois Geometry Lab: Ruoyu Meng, Zihe Wang, Ziqin Xiong, and Hongru Yang.

MC 5479