@MISC{Lago95onthe, author = {Alair Pereira do Lago}, title = {On the Burnside Semigroups . . .}, year = {1995} }

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Abstract

In this paper we prove that the congruence classes of A associated to the Burnside semigroup with jAj generators defined by the equation x n = x n+m , for n 4 and m 1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m = 1 and n 2. De Luca and Varricchio solved the problem for n 5 in 90. A little later, McCammond extended the problem for m 1 and solved it independently in the cases n 6 and m 1. Our work, which is based on the techniques developed by de Luca and Varricchio, extends both these results. We effectively construct a minimal generator \Sigma of our congruence. We introduce an elementary concept, namely the stability of productions, which allows to eliminate all hypothesis related to the values of n and m. A substantial part of our proof consists of showing that all productions in \Sigma are stable, for n 4 and m 1. We also show that \Sigma is a Church-Rosser rewriting system, thus solving the word problem, and sho...