Quasitriangular Structure of Myhill–Nerode Bialgebras

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