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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.
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...
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