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RelativizedNC

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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 thatNC 1 is properly contained inL if and only if there exists an oracleA such thatNC A1 is properly contained inL A. There is an oracleA where the hierarchy collapses,NC A1 = NC A, and another whereNC A1 ⊂NC A2 ⊂ ⋯ ⊂NC A ⊂P A. We then construct anA so that, for anyk, NC A1 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.

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Authors and Affiliations

  1. Department of Computer and Information Science, University of Oregon, 97403, Eugene, OR, USA

    Christopher B. Wilson

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  1. Christopher B. Wilson
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Wilson, C.B. RelativizedNC . Math. Systems Theory 20, 13–29 (1987). https://doi.org/10.1007/BF01692056

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  • DOI: https://doi.org/10.1007/BF01692056

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