@Article{	  DiekertKW12tcs,
  author	= "Volker Diekert and Manfred Kufleitner and Pascal Weil",
  title		= "Star-Free Languages are {Church}-{Rosser} Congruential",
  journal	= "Theoretical Computer Science",
  volume	= "454",
  doi		= "10.1016/j.tcs.2012.01.028",
  year		= "2012",
  pages		= "129--135",
  abstract	= "The class of Church-Rosser congruential languages has been
		  introduced by McNaughton, Narendran, and Otto in 1988. A
		  language L is Church-Rosser congruential (belongs to CRCL),
		  if there is a finite, confluent, and length-reducing
		  semi-Thue system S such that L is a finite union of
		  congruence classes modulo S. To date, it is still open
		  whether every regular language is in CRCL. In this paper,
		  we show that every star-free language is in CRCL. In fact,
		  we prove a stronger statement: For every star-free language
		  L there exists a finite, confluent, and subword-reducing
		  semi-Thue system S such that the total number of congruence
		  classes modulo S is finite and such that L is a union of
		  congruence classes modulo S. The construction turns out to
		  be effective."
}