@Article{	  kl12ijfcs,
  author	= "Kufleitner, Manfred and Lauser, Alexander",
  title		= "Around Dot-Depth One",
  journal	= "International Journal of Foundations of Computer Science",
  year		= "2012",
  publisher	= "World Scientific",
  pages		= "1323--1339",
  volume	= "23",
  number	= "6",
  doi		= "10.1142/S0129054112400552",
  url		= "http://dx.doi.org/10.1142/S0129054112400552",
  abstract	= "The dot-depth hierarchy is a classification of star-free
		  languages. It is related to the quantifier alternation
		  hierarchy of first-order logic over finite words. We
		  consider subclasses of languages with dot-depth 1/2 and
		  dot-depth 1 obtained by prohibiting the specification of
		  prefixes or suffixes. As it turns out, these language
		  classes are in one-to-one arXiv eprintsespondence with
		  fragments of alternation-free first-order logic without
		  min- or max-predicate, respectively. For all fragments, we
		  obtain effective algebraic characterizations. Moreover, we
		  give new proofs for the decidability of the membership
		  problem for dot-depth 1/2 and dot-depth 1."
}