@InProceedings{	  jkl12ciaa:short,
  author	= "Franz Jahn and Manfred Kufleitner and Alexander Lauser",
  title		= "Regular Ideal Languages and Their {B}oolean Combinations",
  booktitle	= "Implementation and Application of Automata (CIAA) 2012,
		  Conference Proceedings",
  series	= "Lecture Notes in Computer Science",
  volume	= "7381",
  publisher	= "Springer",
  pages		= "205--216",
  year		= "2012",
  abstract	= "We consider ideals and Boolean combinations of ideals. For
		  the regular languages within these classes we give
		  expressively complete automaton models. In addition, we
		  consider general properties of regular ideals and their
		  Boolean combinations. These properties include effective
		  algebraic characterizations and lattice identities. In the
		  main part of this paper we consider the following
		  deterministic one-way automaton models: unions of flip
		  automata, weak automata, and Staiger-Wagner automata. We
		  show that each of these models is expressively complete for
		  regular Boolean combination of right ideals. Right ideals
		  over finite words resemble the open sets in the Cantor
		  topology over infinite words. An omega-regular language is
		  a Boolean combination of open sets if and only if it is
		  recognizable by a deterministic Staiger-Wagner automaton;
		  and our result can be seen as a finitary version of this
		  classical theorem. In addition, we also consider the
		  canonical automaton models for right ideals, prefix- closed
		  languages, and factorial languages. In the last section, we
		  consider a two-way automaton model which is known to be
		  expressively complete for two-variable first-order logic.
		  We show that the above concepts can be adapted to these
		  two-way automata such that the resulting languages are the
		  right ideals (resp. prefix-closed languages, resp. Boolean
		  combinations of right ideals) definable in two-variable
		  first-order logic.",
  doi		= "10.1007/978-3-642-31606-7_18"
}