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Axioms 2012, 1(2), 155-172; doi:10.3390/axioms1020155
Article

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)
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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 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).
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Underwood, R.G. Quasitriangular Structure of Myhill–Nerode Bialgebras. Axioms 2012, 1, 155-172.

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