Logically defined subsets of INk
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 ACC0 are discussed.
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