McCammond's normal forms for free aperiodic semigroups revisited

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.Pessoa French-Portuguese project Egide-Grices 11113YMEuropean Regional Development Fund, through the programme COMPETEEuropean Community Fund FEDERANR 2010 BLAN 0202 01 FRE