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arXiv · 1406.0888

McCammond's normal forms for free aperiodic semigroups revisited

Jorge Almeida·José Carlos Costa·Marc Zeitoun
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Abstract

This paper revisits the solution of the word problem for $\omega$-terms interpreted over finite aperiodic semigroups, obtained by J. McCammond. The original proof of correctness of McCammond's algorithm, based on normal forms for such terms, uses McCammond's solution of the word problem for certain Burnside semigroups. In this paper, we establish a new, simpler, correctness proof of McCammond's algorithm, based on properties of certain regular languages associated with the normal forms. This method leads to new applications.

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Jorge Almeida, José Carlos Costa, Marc Zeitoun. 2014-06-03. McCammond's normal forms for free aperiodic semigroups revisited. https://doi.org/10.1112/s1461157014000448

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