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

Quasitriangular Structure of Myhill–Nerode Bialgebras

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Received: 20 June 2012; in revised form: 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)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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MDPI and ACS Style

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

AMA Style

Underwood RG. Quasitriangular Structure of Myhill–Nerode Bialgebras. Axioms. 2012; 1(2):155-172.

Chicago/Turabian Style

Underwood, Robert G. 2012. "Quasitriangular Structure of Myhill–Nerode Bialgebras." Axioms 1, no. 2: 155-172.

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