@InProceedings{	  dkl10dlt,
  title		= "Rankers over Infinite Words ({Extended} Abstract)",
  author	= "Luc Dartois and Manfred Kufleitner and Alexander Lauser",
  bibdate	= "2010-08-18",
  bibsource	= "DBLP,
		  http://dblp.uni-trier.de/db/conf/dlt/dlt2010.html#DartoisKL10",
  booktitle	= "Developments in Language Theory, 14th International
		  Conference ({DLT}) 2010, Conference Proceedings",
  event_place	= "London, ON, Canada",
  event_name	= "Developments in Language Theory, 14th International
		  Conference",
  event_date	= "August 17--20, 2010",
  publisher	= "Springer",
  year		= "2010",
  volume	= "6224",
  editor	= "Yuan Gao and Hanlin Lu and Shinnosuke Seki and Sheng Yu",
  isbn		= "978-3-642-14454-7",
  pages		= "148--159",
  series	= "Lecture Notes in Computer Science",
  url		= "http://dx.doi.org/10.1007/978-3-642-14455-4",
  abstract	= "We consider the fragments $\mathrm{FO}^{2}$,
		  $\mathrm{FO}^{2} \cap \Sigma_{2}$, $\mathrm{FO}^{2} \cap
		  \Pi_{2}$, and $\Delta_{2}$ of first-order logic
		  $\mathrm{FO}[<]$ over finite and infinite words. For all
		  four fragments, we give characterizations in terms of
		  rankers. In particular, we generalize the notion of a
		  ranker to infinite words in two possible ways. Both
		  extensions are natural in the sense that over finite words,
		  they coincide with classical rankers and over infinite
		  words, they both have the full expressive power of
		  $\mathrm{FO}^{2}$. Moreover, the first extension of rankers
		  admits a characterization of $\mathrm{FO}^{2} \cap
		  \Sigma_{2}$ while the other leads to a characterization of
		  $\mathrm{FO}^{2} \cap \Pi_{2}$. Both versions of rankers
		  yield characterizations of the fragment $\Delta_{2} =
		  \Sigma_{2} \cap \Pi_{2}$. As a byproduct, we also obtain
		  characterizations based on unambiguous temporal logic and
		  unambiguous interval temporal logic.",
  doi		= "10.1007/978-3-642-14455-4_15"
}