Algebra-coalgebra duality in brzozowski's minimization algorithm-Reference-Cited by-同舟云学术

Algebra-coalgebra duality in brzozowski's minimization algorithm

Published:2014-02 Issue:1 Volume:15 Page:1-29
ISSN:1529-3785
Container-title:ACM Transactions on Computational Logic
language:en
Short-container-title:ACM Trans. Comput. Logic

Author:

Bonchi Filippo¹,Bonsangue Marcello M.²,Hansen Helle H.³,Panangaden Prakash⁴,Rutten Jan J. M. M.⁵,Silva Alexandra³

Affiliation:

1. ENS Lyon, Université de Lyon LIP (UMR 5668), France

2. LIACS - Leiden University, The Netherlands

3. Radboud University Nijmegen, The Netherlands

4. McGill University, Quebec, Canada

5. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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.

Funder

Natural Sciences and Engineering Research Council of Canada

Centre National de la Recherche Scientifique

Agence Nationale de la Recherche

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Fundação para a Ciência e a Tecnologia

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/2490818

Reference36 articles.

1. On the relevance of abstract algebra to control theory

2. Machines in a Category: An Expository Introduction

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