We present a protocol that transforms any quantum multi-prover interactive proof into a
nonlocal game in which questions consist of logarithmic number of bits and answers of …

We define a new notion of “robust simulations” between complexity classes which is
intermediate between the traditional notions of infinitely-often and almost-everywhere, as …

This thesis focuses on problems in the theory and practice of machine learning and big data.
We will explore the complexity-theoretic properties of MapReduce, one of the most …

This dissertation presents several results in fine-grained complexity. Fine-grained
complexity aims at extending traditional complexity theory by making more precise, and fine …

These are notes for the Spring 2020 semester of the Yale course CPSC 468/568
Computational Complexity. This document also incorporates the lecture schedule and …

We show time hierarchies for reasonable semantic classes without advice by eliminating the
constant bits of advice in previous results. The elimination is done by a contrapositive …

This work is devoted to explore the novel method of proving circuit lower bounds for the
class NEXP by Ryan Williams. Williams is able to show two circuit lower bounds: A …

When Thomas Schwentick first introduced me to context-free games, they were originally
just supposed to be a little side project for me while I was looking for a suitable topic for my …

After many years of effort, the main questions of complexity theory remain unresolved, even
though the concepts involved are simple. Understanding the main idea behind the statement …

We formulate a very general tight diagonalization method for the Blum complexity measures
satisfying two additional axioms related to our diagonalizer machine. We apply this method …