Abstract
We give a characterization, in terms of a restriction of semi-simple sets, of the class of subsets of IN k definable in an extension of first-order logic obtained by adjoining quantifiers which count modulo an integer. It is shown that this class strictly contains the class of recognizable subsets of IN k and is strictly contained in the class of rational subsets of IN K. Links with the parallel complexity class ACC 0 are discussed.
Research supported by the Natural Sciences and Engineering Research Council of Canada, and by the PRC Mathématique et Informatique, France.
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© 1989 Springer-Verlag Berlin Heidelberg
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Péladeau, P. (1989). Logically defined subsets of IN k . In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_87
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DOI: https://doi.org/10.1007/3-540-51486-4_87
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