k-counting automata
In this paper, we define -counting automata as recognizers for -languages, languages of infinite words. We prove that the class of -languages they recognize is a proper extension of the -regular languages. In addition we prove that languages recognized by -counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for -counting automata. However, we conjecture strongly that it is decidable and give formal reasons why we believe so.