Brzozowski's algorithm (co)algebraically

Authors:
Filippo Bonchi;Marcello M. Bonsangue;Jan J. M. M. Rutten;Alexandra Silva
Affiliations:
CNRS, ENS Lyon, Université de Lyon LIP (UMR 5668), France;LIACS, Leiden University, The Netherlands,Radboud University Nijmegen, The Netherlands;Radboud University Nijmegen, The Netherlands,Centrum Wiskunde & Informatica, The Netherlands;Radboud University Nijmegen, The Netherlands,Centrum Wiskunde & Informatica, The Netherlands,HASLab / INESC TEC, Universidade do Minho, Portugal
Venue:
Logic and Program Semantics
Year:
2012

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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 the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations.