<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Alexandra Silva</style></author><author><style face="normal" font="default" size="100%">Filippo Bonchi</style></author><author><style face="normal" font="default" size="100%">Marcello Bonsangue</style></author><author><style face="normal" font="default" size="100%">Helle Hvid Hansen</style></author><author><style face="normal" font="default" size="100%">Prakash Panangaen</style></author><author><style face="normal" font="default" size="100%">Jan Rutten</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Algebra- Coalgebra Duality in Brzozowski's Minimization Algorithm</style></title><secondary-title><style face="normal" font="default" size="100%">ACM Transactions on Computacional Logic</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://haslab.uminho.pt/sites/default/files/xana/files/bonchi_algebra.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">ACM</style></publisher><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">1-29</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Duality plays a fundamental role in many areas of mathematics, computer science, systems&lt;br /&gt;
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.&lt;/p&gt;
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