%0 Journal Article
%J ACM Transactions on Computacional Logic
%D 2014
%T Algebra- Coalgebra Duality in Brzozowski's Minimization Algorithm
%A Alexandra Silva
%A Filippo Bonchi
%A Marcello Bonsangue
%A Helle Hvid Hansen
%A Prakash Panangaen
%A Jan Rutten
%I ACM
%N 1
%P 1-29
%V 15
%X <p>Duality plays a fundamental role in many areas of mathematics, computer science, systems<br /> theory and even physics. For example, the familiar concept of Fourier transform is essentially a duality result: an instance of Pontryagin duality, see, for example the standard textbook [Rudin 1962]. Another basic instance, known to undergraduates, is the duality of a finite-dimensional vector spaces V over some field k, and the space of linear maps from V to k, which is itself a finite-dimensional vector space. Building on this self-duality, a fundamental principle in systems theory due to [Kalman 1959] captures the duality between the concepts of observability and controllability (to be explained below). The latter was further extended to automata theory (where controllability amounts to reachability) in [Arbib and Zeiger 1969], and in various papers [Arbib and Manes 1974; 1975a; 1975c; 1975b; 1980a; 1980b] where Arbib and Manes explored algebraic automata theory in a categorical framework; see also the excellent collection of papers [Kalman et al. 1969] where both automata theory and systems theory is presented.</p>
%> https://haslab.uminho.pt/sites/default/files/xana/files/bonchi_algebra.pdf