Abstract
The paper discusses results on ω-languages in a recursion theoretic framework which is adapted to the treatment of formal languages. We consider variants of the arithmetical hierarchy which are not based on the recursive sets but on sets defined in terms of finite automata. In particular, it is shown how the theorems of Büchi and McNaughton on regular ω-languages can be viewed as results on collapsing such quantifier hierarchies. Further automata theoretic hierarchies are outlined.
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© 1989 Springer-Verlag Berlin Heidelberg
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Thomas, W. (1989). Automata and quantifier hierarchies. In: Pin, J.E. (eds) Formal Properties of Finite Automata and Applications. LITP 1988. Lecture Notes in Computer Science, vol 386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013115
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DOI: https://doi.org/10.1007/BFb0013115
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