Brzozowski's Algorithm (Co)Algebraically.
Filippo Bonchi, Marcello Bonsangue, Jan Rutten, Alexandra Silva · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2012
Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. 1