Modularity in the Semilattice of ω-Words. (15th May 2014) - Buls, Jānis; Cers, Edmunds
Abstract : 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 leastℵ 0 . 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.