Modularity in the Semilattice of ω-Words. (15th May 2014)

• Record Type: Journal Article
• Authors: Buls, Jānis; Cers, Edmunds
• Other Names: Kamae Teturo Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2014(2014)
• Publication Date: 2014-05-15
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2014/891760
• Languages: English
• ISSNs: 2090-9837

Abstract

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.