On differential privacy and adaptive data analysis with bounded space
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 …
data analysis. Specifically, Under standard cryptographic assumptions, we show that there …
Simulation theorems via pseudo-random properties
We generalize the deterministic simulation theorem of Raz & McKenzie (Combinatorica 19
(3): 403–435, 1999), to any gadget which satisfies a certain hitting property. We prove that …
(3): 403–435, 1999), to any gadget which satisfies a certain hitting property. We prove that …
MaxSAT resolution and subcube sums
We study the MaxSAT Resolution (MaxRes) rule in the context of certifying unsatisfiability.
We show that it can be exponentially more powerful than tree-like resolution, and when …
We show that it can be exponentially more powerful than tree-like resolution, and when …
Query-to-communication lifting using low-discrepancy gadgets
Lifting theorems are theorems that relate the query complexity of a function f:{0,1\}^n→{0,1\}
to the communication complexity of the composed function f∘g^n for some “gadget” …
to the communication complexity of the composed function f∘g^n for some “gadget” …
Lifting with simple gadgets and applications to circuit and proof complexity
We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to
monotone span program size by Pitassi and Robere (2018) so that it works for any gadget …
monotone span program size by Pitassi and Robere (2018) so that it works for any gadget …
Query-to-communication lifting for BPP using inner product
We prove a new query-to-communication lifting for randomized protocols, with inner product
as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting …
as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting …
Lifting theorems meet information complexity: Known and new lower bounds of set-disjointness
G Yang, J Zhang - arxiv preprint arxiv:2309.13517, 2023 - arxiv.org
Set-disjointness problems are one of the most fundamental problems in communication
complexity and have been extensively studied in past decades. Given its importance, many …
complexity and have been extensively studied in past decades. Given its importance, many …
Randomized versus deterministic decision tree size
A classic result of Nisan [SICOMP'91] states that the deterministic decision tree* depth*
complexity of every total Boolean function is at most the cube of its randomized decision …
complexity of every total Boolean function is at most the cube of its randomized decision …
The demand query model for bipartite matching
N Nisan - Proceedings of the 2021 ACM-SIAM Symposium on …, 2021 - SIAM
We introduce a “concrete complexity” model for studying algorithms for matching in bipartite
graphs. The model is based on the “demand query” model used for combinatorial auctions …
graphs. The model is based on the “demand query” model used for combinatorial auctions …
Space characterizations of complexity measures and size-space trade-offs in propositional proof systems
T Papamakarios, A Razborov - Journal of Computer and System Sciences, 2023 - Elsevier
We identify two new clusters of proof complexity measures equal up to polynomial and log
n factors. The first cluster contains the logarithm of tree-like resolution size, regularized …
n factors. The first cluster contains the logarithm of tree-like resolution size, regularized …