Mathematical systems theory

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


  • Christopher B. Wilson


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.


Computational Mathematic Relativize Depth Relativize Space Circuit Family Uniform Family 
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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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