Algebra-coalgebra duality in brzozowski's minimization algorithm

Filippo Bonchi, Marcello M. Bonsangue, Helle H. Hansen, Prakash Panangaden, Jan J. M. M. Rutten, Alexandra Silva
2014 ACM Transactions on Computational Logic  
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, non-deterministic and weighted automata.
more » ... c and weighted automata.
doi:10.1145/2490818 fatcat:jaj7lqxbcvcfdebm6bkdygwjk4