Axioms 2012, 1(2), 155-172; doi:10.3390/axioms1020155
Quasitriangular Structure of Myhill–Nerode Bialgebras
Department of Mathematics/Informatics Institute, Auburn University Montgomery, P.O. Box 244023, Montgomery, AL 36124, USA
Received: 20 June 2012 / Revised: 15 July 2012 / Accepted: 17 July 2012 / Published: 24 July 2012
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations)
Abstract
In computer science the Myhill–Nerode Theorem states that a set L of words in a finite alphabet is accepted by a finite automaton if and only if the equivalence relation ∼L, defined as x ∼L y if and only if xz ∈ L exactly when yz ∈ L, ∀z, has finite index. The Myhill–Nerode Theorem can be generalized to an algebraic setting giving rise to a collection of bialgebras which we call Myhill–Nerode bialgebras. In this paper we investigate the quasitriangular structure of Myhill–Nerode bialgebras.Keywords:
algebra; coalgebra; bialgebra; Myhill–Nerode theorem; Myhill–Nerode bialgebra; quasitriangular structure
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
Scifeed alert for new publications
Never miss any articles matching your research from any publisher- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Share & Cite This Article
MDPI and ACS Style
Underwood, R.G. Quasitriangular Structure of Myhill–Nerode Bialgebras. Axioms 2012, 1, 155-172.