The omega-inequality problem for concatenation hierarchies of star-free   languages
  The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half) levels of the Straubing-Th\'erien hierarchy. 
J. Almeida, O. Kl\'ima, M. Kunc
math.GR cs.FL