Commit dd0a176d authored by James's avatar James

Add Latex source for a talk I gave (virtually) at IAS.

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This is a talk I gave (virtually) at IAS 2020-04-06. To see the (extensive)
speaker's notes, add "\setbeameroption{show notes}" to talk.tex somewhere
between documentclass and begin{document}, and recompile.
Recording: https://video.ias.edu/csdm/2020/0406-JamesCook
Talk title: Borrowing memory that's being used: catalytic approaches
tothe Tree Evaluation Problem
Abstract:
I'll be presenting some joint work with Ian Mertz scheduled to appear at
STOC 2020.
The study of the Tree Evaluation Problem (TEP), introduced by S. Cook et
al. (TOCT 2012), is a promising approach to separating L from P. Given a
label in [k] at each leaf of a complete binary tree and an explicit
function in [k]^2 -> [k] for recursively computing the value of each
internal node from its children, the problem is to compute the value at
the root node. A simple recursive algorithm can solve this using
Theta(h log k) memory, where h is the tree height and k is the size of
the alphabet. Until now, no better deterministic algorithm was known.
We present a new algorithm which uses less memory when k is not too big
compared to h, inspired by a surprising result from Burhman et al. about
"catalytic space" computation (STOC 2012). Ours is the first algorithm
to beat the simple recursive algorithm, and also the first non-trivial
approach to proving a deterministic upper bound for TEP.
% Common preamble for the tests in this repository.
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\RequirePackage{tikz}
\usetikzlibrary{automata,backgrounds,overlay-beamer-styles,shapes}
% For referencing pause values from different parts of a frame.
% https://tex.stackexchange.com/a/50493
\makeatletter
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\newcommand*{\pauseentry}[3]{\global\@namedef{[email protected]#[email protected]#2}{#3}}
\makeatother
% Styles for highlighting nodes and edges in a graph.
\tikzset{%
hlnode/.style={fill=blue!20!white,fill on={#1}},%
hledge/.style={%
background default aspect=thin,%
background aspect=thick,%
aspect on={#1},%
background default draw=black,%
background draw=blue,%
draw on={#1},%
background text=blue,%
text on={#1}}}
\newcommand{\ints}{\mathbb{Z}}
% Format a complexity class name.
\newcommand{\ccl}{\operatorname}
\newcommand{\logspace}{\ccl{L}}
\newcommand{\polytime}{\ccl{P}}
% Binary encoding.
\DeclareMathOperator{\binary}{Bin}
% Binary algorithm.
\DeclareMathOperator{\binaryAlg}{ComputeBin}
\DeclareMathOperator{\checkNode}{CheckNode}
% Hybrid encoding.
\DeclareMathOperator{\hybrid}{Hybrid}
% One-hot encoding.
\DeclareMathOperator{\oneHot}{OneHot}
% One hot algorithm.
\DeclareMathOperator{\oneHotAlg}{ComputeOneHot}
\DeclareMathOperator{\tep}{TEP}
% Draws a rotated 3x3 node function. To be used inside a path with the draw style.
\newcommand{\nodeFn}[2]{
{ % Rotate and scale around the current coordinate, +(0,0).
[rotate around={45:+(0,0)},scale around={0.7:+(0,0)}]
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{node at +({\x+0.5},{\y+0.5}) {\nodeContent}}
#2
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\newcommand{\sectiontoc}{\tableofcontents[currentsection]}
\newcommand{\subsectiontoc}{\tableofcontents[currentsection,currentsubsection]}
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