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# The Complexity of ODDnA and MODmnA

• William I. Gasarch
• Georgia A. Martin
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 16)

## Abstract

Recall that, for n ≥ 1, ODD n A is the set of n-tuples (x 1 ,…,x n ) such that # n A (x 1 ,…,x n ) is odd:
$${\rm{ODD}}_n^A = \left\{ {\left( {{x_1}, \ldots ,{x_n}} \right):\# _n^A\left( {{x_1}, \ldots ,{x_n}} \right){\rm{is}}\,{\rm{odd}}{\rm{.}}} \right\}$$
Clearly, ODD n A ∈ QC∥(n,A). If A = K or A is semirecursive, then (by Theorems 2.1.4 and 4.3.2.2, respectively) $${\rm{ODD}}_{{2^n} - 1}^A \in {\rm{Q}}\left( {n,A} \right)$$, hence $${\rm{ODD}}_{{2^n}}^A \in {\rm{Q}}\left( {n + 1,A} \right)$$. Can we do better than this for such A? What about other types of sets A? In this chapter we show the following.

## Keywords

Prove Theorem Algorithm Step Boolean Formula Query Answer Bibliographic Note
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1999

## Authors and Affiliations

• William I. Gasarch
• 1
• Georgia A. Martin
• 2
1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
2. 2.WheatonUSA