Commit dd0a176d authored by James's avatar James

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

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.
Talk title: Borrowing memory that's being used: catalytic approaches
tothe Tree Evaluation Problem
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.
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