Sam van Gool

Dept. of Mathematics, CUNY --- ILLC, University of Amsterdam
Talk Title: 
Language hierarchies and profinite monoids via Stone duality
Event Type: 
Frontiers Talk Series
Fall 2017
Friday, November 17, 2017, 3:30 pm

Finite monoids are useful algebraic invariants for regular languages: logical properties of a regular language correspond to algebraic properties of the finite monoids that recognize it. Profinite monoids figure prominently in this theory as the appropriate inverse limit objects for well-behaved classes of finite monoids. While the theory of (pro)finite monoids and regular languages is very classical, many problems in it remain open. In particular, there are notoriously difficult unanswered questions about the decidability of hierarchies of regular languages defined by restricting quantifier depth. In this talk, I will show how, in the past few years, the mathematical theory of Stone duality has helped to shed new light on some of these problems.