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Complexity Theory Column 89: The Polynomial Hierarchy, Random Oracles, and Boolean Circuits

Published: 01 December 2015 Publication History

Abstract

We give an overview of a recent result [RST15] showing that the polynomial hierarchy is in finite relative to a random oracle. Since the early 1980s it has been known that this result would follow from a certain "average-case depth hierarchy theorem" for Boolean circuits. In this article we present some background and history of related relativized separations; sketch the argument showing how the polynomial hierarchy result follows from the circuit lower bound; and explain the techniques underlying the new circuit lower bound.

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  1. Complexity Theory Column 89: The Polynomial Hierarchy, Random Oracles, and Boolean Circuits

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    cover image ACM SIGACT News
    ACM SIGACT News  Volume 46, Issue 4
    December 2015
    103 pages
    ISSN:0163-5700
    DOI:10.1145/2852040
    Issue’s Table of Contents
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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    Publication History

    Published: 01 December 2015
    Published in SIGACT Volume 46, Issue 4

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