Abstract

The notion of frequency computation captures the class\Omega of all sets A such that for some n, the n-fold characteristic function of A can be computed with fewer than n errors. We consider the recursion theoretic properties of\Omega with special emphasis on recursively enumerable sets. 1 Introduction In this paper we study properties of sets that possess an "effective structure" such that their characteristic function can be recursively approximated in a certain sense. We consider approximations given by frequency computation and bounded queries as explained below. The notion of frequency computation was introduced by Rose [31] in the early sixties. For natural numbers m;n 1, m n, a set A is called (m; n)-recursive (in short A 2 \Omega\Gamma m;n)) iff there is a recursive function f : ! n ! f0; 1g n , mapping n-tuples of numbers to n-tuples of bits, such that for any n pairwise distinct numbers x 1 ; : : : ; x n : f(x 1 ; : : : ; x n ) = (b 1 ; : : : ; b n ) ) jfi : ØA (x ...

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