Complexity Theory Column 89-Reference-Cited by-同舟云学术

Complexity Theory Column 89

Published:2015-12 Issue:4 Volume:46 Page:50-68
ISSN:0163-5700
Container-title:ACM SIGACT News
language:en
Short-container-title:SIGACT News

Author:

Rossman Benjamin¹,Servedio Rocco A.²,Tan Li-Yang³

Affiliation:

1. National Institute of Informatics, Tokyo

2. Columbia University

3. Toyota Technological Institute at Chicago

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.

Publisher

Association for Computing Machinery (ACM)

Link

https://dl.acm.org/doi/pdf/10.1145/2852040.2852052

Reference44 articles.

1. Scott Aaronson. The Complexity Zoo. Available at http://cse.unl.edu/~cbourke/latex/ComplexityZoo.pdf. 2.1 Scott Aaronson. The Complexity Zoo. Available at http://cse.unl.edu/~cbourke/latex/ComplexityZoo.pdf. 2.1

2. A counterexample to the generalized Linial-Nisan conjecture;Aaronson Scott;Electronic Colloquium on Computational Complexity,2010

3. BQP and the polynomial hierarchy

4. ∑11-Formulae on finite structures

5. Random oracles separate PSPACE from the polynomial-time hierarchy

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1. An Average-Case Depth Hierarchy Theorem for Boolean Circuits;Journal of the ACM;2017-10-15

2. Local Restrictions from the Furst-Saxe-Sipser Paper;Theory of Computing Systems;2016-11-29