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Mathematical systems theory

, Volume 20, Issue 1, pp 13–29 | Cite as

RelativizedNC

  • Christopher B. Wilson
Article

Abstract

This paper introduces a notion of relativized depth for circuit families and discusses issues regarding uniform families of relativized circuits. This allows us to define a version of relativizedNC and compare it under various oracles with relativizedL, NL, andP. We see thatNC1 is properly contained inL if and only if there exists an oracleA such thatNC 1 A is properly contained inL A . There is an oracleA where the hierarchy collapses,NC 1 A = NC A , and another whereNC 1 A NC 2 A ⊂ ⋯ ⊂NC A P A . We then construct anA so that, for anyk, NC 1 A contains a set not inNSPACE A (O(n k )), suggesting that the notion of relativized space is too weak or that of relativized depth is too strong.

Keywords

Computational Mathematic Relativize Depth Relativize Space Circuit Family Uniform Family 
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-Verlag New York Inc 1987

Authors and Affiliations

  • Christopher B. Wilson
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of OregonEugeneUSA

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