The Parametric Ordinal-Recursive Complexity of Post Embedding Problems
  Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet. 
Prateek Karandikar and Sylvain Schmitz
cs.LO