Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 891760, 6 pages
Research Article

Modularity in the Semilattice of ω-Words

Department of Mathematics, University of Latvia, 19 Rainis Boulevard, Riga 1586, Latvia

Received 31 August 2013; Accepted 6 December 2013; Published 15 May 2014

Academic Editor: Teturo Kamae

Copyright © 2014 Jānis Buls and Edmunds Cers. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A partial ordering of ω-words can be introduced with regard to whether an ω-word can be transformed into another by a Mealy machine. It is known that the poset of ω-words that is introduced by this ordering is a join-semilattice. The width of this join-semilattice has the power of continuum while the depth is at least . We have created a technique for proving that power-characteristic ω-words are incomparable. We use this technique to show that this join-semilattice is not modular.