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

Prefix Guaran 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations