Finite acceptance of infinite words

I. Litovsky, L. Staiger

	   In this paper we consider the following two types of finite
	   acceptance of infinite words by finite automata: An infinite
	   word $\xi$ is accepted if and only if there is a run on input
	   $\xi$ for which an accepting state is visited at least once
	   or at least once but only finitely often.  The resulting
	   classes of regular $\omega$-languages are characterized by
	   language-theoretic means, and they are positioned into the
	   known hierarchies of regular $\omega$-languages.