Bonchi F, Bonsangue M, Rutten J, Silva A.  2012.  Brzozowski's Algorithm (Co)Algebraically. Logic and Program Semantics - Essays Dedicated to Dexter Kozen on the Occasion of His 60th Birthday. 7230:12–23. AbstractWebsite

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.