Semialgebraic proofs and efficient algorithm design

N Fleming, P Kothari, T Pitassi - Foundations and Trends® in …, 2019 - nowpublishers.com
Over the last twenty years, an exciting interplay has emerged between proof systems and
algorithms. Some natural families of algorithms can be viewed as a generic translation from …

Random oracles and non-uniformity

S Coretti, Y Dodis, S Guo, J Steinberger - Annual International Conference …, 2018 - Springer
We revisit security proofs for various cryptographic primitives in the auxiliary-input random-
oracle model (AI-ROM), in which an attacker\mathcal A can compute arbitrary S bits of …

Deterministic communication vs. partition number

M Göös, T Pitassi, T Watson - 2015 IEEE 56th Annual …, 2015 - ieeexplore.ieee.org
We show that deterministic communication complexity can be super logarithmic in the
partition number of the associated communication matrix. We also obtain near-optimal …

On differential privacy and adaptive data analysis with bounded space

I Dinur, U Stemmer, DP Woodruff, S Zhou - … International Conference on …, 2023 - Springer
We study the space complexity of the two related fields of differential privacy and adaptive
data analysis. Specifically, Under standard cryptographic assumptions, we show that there …

Query-to-communication lifting for BPP

M Göös, T Pitassi, T Watson - 2017 IEEE 58th Annual …, 2017 - ieeexplore.ieee.org
For any n-bit boolean function f, we show that the randomized communication complexity of
the composed function fog n, where g is an index gadget, is characterized by the …

Communication complexity of approximate Nash equilibria

Y Babichenko, A Rubinstein - Proceedings of the 49th Annual ACM …, 2017 - dl.acm.org
For a constant ϵ, we prove a (N) lower bound on the (randomized) communication
complexity of ϵ-Nash equilibrium in two-player N x N games. For n-player binary-action …

Monotone circuit lower bounds from resolution

A Garg, M Göös, P Kamath, D Sokolov - Proceedings of the 50th Annual …, 2018 - dl.acm.org
For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we
show that a gadget-composed version of F is hard to refute in any proof system whose lines …

Dimension-free bounds and structural results in communication complexity

L Hambardzumyan, H Hatami, P Hatami - Israel Journal of Mathematics, 2023 - Springer
The purpose of this article is to initiate a systematic study of dimension-free relations
between basic communication and query complexity measures and various matrix norms. In …

Non-uniform bounds in the random-permutation, ideal-cipher, and generic-group models

S Coretti, Y Dodis, S Guo - Advances in Cryptology–CRYPTO 2018: 38th …, 2018 - Springer
The random-permutation model (RPM) and the ideal-cipher model (ICM) are idealized
models that offer a simple and intuitive way to assess the conjectured standard-model …

Approximating rectangles by juntas and weakly-exponential lower bounds for LP relaxations of CSPs

PK Kothari, R Meka, P Raghavendra - … of the 49th Annual ACM SIGACT …, 2017 - dl.acm.org
We show that for constraint satisfaction problems (CSPs), sub-exponential size linear
programming relaxations are as powerful as n Ω (1)-rounds of the Sherali-Adams linear …