Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/34733
Título: | Algebra - coalgebra duality in Brzozowski's minimization algorithm |
Autor(es): | Bonchi, Filippo Rutten, Jan Panangaen, Prakash Silva, Alexandra M. Bonsangue, Marcello Hansen, Helle Hvid |
Palavras-chave: | Algorithms Theory Algebra automata coalgebra duality |
Data: | Fev-2014 |
Editora: | Association for Computing Machinery (ACM) |
Revista: | ACM Transactions on Computational Logic |
Resumo(s): | Duality plays a fundamental role in many areas of mathematics, computer science, systems 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. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/34733 |
DOI: | 10.1145/2490818 |
ISSN: | 1529-3785 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | HASLab - Artigos em revistas internacionais |