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Algebra-coalgebra duality in brzozowski's minimization algorithm

Algebra-coalgebra duality in brzozowski's minimization algorithm Algebra-Coalgebra Duality in Brzozowski's Minimization Algorithm FILIPPO BONCHI, ENS Lyon, Universit´ de Lyon LIP (UMR 5668) e MARCELLO M. BONSANGUE, LIACS - Leiden University HELLE H. HANSEN, Radboud University Nijmegen PRAKASH PANANGADEN, McGill University JAN J. M. M. RUTTEN, Centrum Wiskunde & Informatica ALEXANDRA SILVA, Radboud University Nijmegen 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 a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algorithms to obtain minimal language equivalent automata from Moore nondeterministic and weighted automata. Categories and Subject Descriptors: F.1.1 [Computation by Abstract Devices]: Models of Computation; F.4.3 [Mathematical Logic and Formal Languages]: Formal Languages; I.1.2 [Symbolic and Algebraic Manipulation]: Algorithms General Terms: Algorithms, Theory Additional Key Words and Phrases: Algebra, automata, coalgebra, duality ACM Reference Format: F. Bonchi, M. M. Bonsangue, H. H. Hansen, P. Panangaden, J. J. M. M. Rutten, and A. Silva. 2014. Algebracoalgebra duality in Brzozowski's minimization algorithm. ACM Trans. Comput. Logic 15, 1, Article 3 (February 2014), 29 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Algebra-coalgebra duality in brzozowski's minimization algorithm

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References (42)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2490818
Publisher site
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Abstract

Algebra-Coalgebra Duality in Brzozowski's Minimization Algorithm FILIPPO BONCHI, ENS Lyon, Universit´ de Lyon LIP (UMR 5668) e MARCELLO M. BONSANGUE, LIACS - Leiden University HELLE H. HANSEN, Radboud University Nijmegen PRAKASH PANANGADEN, McGill University JAN J. M. M. RUTTEN, Centrum Wiskunde & Informatica ALEXANDRA SILVA, Radboud University Nijmegen 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 a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algorithms to obtain minimal language equivalent automata from Moore nondeterministic and weighted automata. Categories and Subject Descriptors: F.1.1 [Computation by Abstract Devices]: Models of Computation; F.4.3 [Mathematical Logic and Formal Languages]: Formal Languages; I.1.2 [Symbolic and Algebraic Manipulation]: Algorithms General Terms: Algorithms, Theory Additional Key Words and Phrases: Algebra, automata, coalgebra, duality ACM Reference Format: F. Bonchi, M. M. Bonsangue, H. H. Hansen, P. Panangaden, J. J. M. M. Rutten, and A. Silva. 2014. Algebracoalgebra duality in Brzozowski's minimization algorithm. ACM Trans. Comput. Logic 15, 1, Article 3 (February 2014), 29

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Feb 1, 2014

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