Chapter

Logic and Program Semantics

Volume 7230 of the series Lecture Notes in Computer Science pp 12-23

Brzozowski’s Algorithm (Co)Algebraically

  • Filippo BonchiAffiliated withCNRS, ENS Lyon, Université de Lyon LIP (UMR 5668)
  • , Marcello M. BonsangueAffiliated withLIACS, Leiden UniversityRadboud University Nijmegen
  • , Jan J. M. M. RuttenAffiliated withRadboud University NijmegenCentrum Wiskunde & Informatica
  • , Alexandra SilvaAffiliated withRadboud University NijmegenCentrum Wiskunde & InformaticaHASLab / INESC TEC, Universidade do Minho

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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.