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)


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, 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.


Prefix Guaran 


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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

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