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k-counting automata

Published online by Cambridge University Press:  10 October 2012

Joël Allred  and
Ulrich Ultes-Nitsche
Joël Allred
Affiliation:
Department of Computer Science, University of Fribourg, Boulevard de Pérolles 90, 1700 Fribourg, Switzerland,. joel.allred@unifr.ch, uun@unifr.ch.
Ulrich Ultes-Nitsche
Affiliation:
Department of Computer Science, University of Fribourg, Boulevard de Pérolles 90, 1700 Fribourg, Switzerland,. joel.allred@unifr.ch, uun@unifr.ch.
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Abstract

In this paper, we define k-counting automata as recognizers forω-languages, i.e. languages of infinite words. Weprove that the class of ω-languages they recognize is a proper extensionof the ω-regular languages. In addition we prove that languagesrecognized by k-counting automata are closed under Boolean operations. Itremains an open problem whether or not emptiness is decidable fork-counting automata. However, we conjecture strongly that it is decidableand give formal reasons why we believe so.

Keywords

ω-automataextensions to regularω-languagesclosure under Boolean operationsemptiness probleminfinite hierarchy ofω-languages
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 4: Special Issue: Non-Classical Models ofAutomata and Applications III (NCMA-2011) , October 2012 , pp. 461 - 478
Copyright
© EDP Sciences 2012

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