This project is concerned with equations on varieties of finite monoids. Level k of Straubing's hierarchy of aperiodic monoids can be parametrized in a natural way giving a sequence of varieties of monoids. Eilenberg and Schutzenberger have shown that varieties of monoids can be described in terms of equations. Simon has given equational characterizations for the varieties which has been extended by Blanchet-Sadri. One of the questions of this research project is to determine equations describing other varieties. The study of equations on certain varieties is closely related to the study of Ehrenfeucht-Fraisse games, and sequential functions and the wreath product. These equational formulations can be applied to problems in language theory.
