Algebra-coalgebra duality in brzozowski's minimization algorithm

Authors:
Filippo Bonchi;Marcello M. Bonsangue;Helle H. Hansen;Prakash Panangaden;Jan J. M. M. Rutten;Alexandra Silva
Affiliations:
ENS Lyon, Université de Lyon LIP (UMR 5668), France;LIACS - Leiden University, The Netherlands;Radboud University Nijmegen, The Netherlands;McGill University, Quebec, Canada;Centrum Wiskunde & Informatica, Amsterdam, The Netherlands;Radboud University Nijmegen, The Netherlands
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2014

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Abstract

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.