k-counting automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 4, pp. 461-478.

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

DOI : 10.1051/ita/2012021
Classification : 68Q45, 20F10
Mots-clés : ω-automata, extensions to regularω-languages, closure under boolean operations, emptiness problem, infinite hierarchy ofω-languages 
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     author = {Allred, Jo\"el and Ultes-Nitsche, Ulrich},
     title = {$k$-counting automata},
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Allred, Joël; Ultes-Nitsche, Ulrich. $k$-counting automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 4, pp. 461-478. doi : 10.1051/ita/2012021. http://archive.numdam.org/articles/10.1051/ita/2012021/

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