Abstract
We consider analogues of the arithmetical hierarchy over word relations, obtained by replacing the class of recursive relations with some other classes which are defined by various types of finite and pushdown automata or by concatenation formulas.
Most of the new hierarchies turn out to be downward prolongations of the arithmetical hierarchy: They reach the class of recursive relations at their second level. The lower levels of the different new hierarchies are shown to be incomparable w.r.t. set inclusion for the most part.
This work is partially supported by ESPRIT Basic Research Action 3166 ‘Algebraic and Syntactic Methods In Computer Science’ (ASMICS)
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Seibert, S. (1992). Quantifier hierarchies over word relations. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023779
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DOI: https://doi.org/10.1007/BFb0023779
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