## Quantifying the Amount of Verboseness (1995)

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Citations: | 16 - 6 self |

### BibTeX

@MISC{Beigel95quantifyingthe,

author = {Richard Beigel and Martin Kummer and Frank Stephan},

title = {Quantifying the Amount of Verboseness},

year = {1995}

}

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### Abstract

We study the fine structure of the classification of sets of natural numbers A according to the number of queries which are needed to compute the n-fold characteristic function of A. A complete characterization is obtained, relating the question to finite combinatorics. In order to obtain an explicit description we consider several interesting combinatorial problems. 1 Introduction In the theory of bounded queries, we measure the complexity of a function by the number of queries to an oracle which are needed to compute it. The field has developed in various directions, both in complexity theory and in recursion theory; see Gasarch [21] for a recent survey. One of the original concerns is the classification of sets A of natural numbers by their "query complexity," i.e., according to the number of oracle queries that are needed to compute the n-fold characteristic function F A n = x 1 ; : : : ; x n : (ØA (x 1 ); : : : ; ØA (x n )). In [3, 8] a set A is called verbose iff F A n is com...