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Electronic Colloquium on Computational Complexity

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All reports by Author Marco Carmosino:

TR18-095 | 11th May 2018
Marco Carmosino, Russell Impagliazzo, Shachar Lovett, Ivan Mihajlin

Hardness Amplification for Non-Commutative Arithmetic Circuits

We show that proving mildly super-linear lower bounds on non-commutative arithmetic circuits implies exponential lower bounds on non-commutative circuits. That is, non-commutative circuit complexity is a threshold phenomenon: an apparently weak lower bound actually suffices to show the strongest lower bounds we could desire.

This is part of a recent ... more >>>

TR18-092 | 4th May 2018
Marco Carmosino, Russell Impagliazzo, Manuel Sabin

Fine-Grained Derandomization: From Problem-Centric to Resource-Centric Complexity

We show that popular hardness conjectures about problems from the field of fine-grained complexity theory imply structural results for resource-based complexity classes. Namely, we show that if either k-Orthogonal Vectors or k-CLIQUE requires $n^{\epsilon k}$ time, for some constant $\epsilon > 1/2$, to count (note that these conjectures are significantly ... more >>>

TR16-008 | 26th January 2016
Marco Carmosino, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova

Algorithms from Natural Lower Bounds

Circuit analysis algorithms such as learning, SAT, minimum circuit size, and compression imply circuit lower bounds. We show a generic implication in the opposite direction: natural properties (in the sense of Razborov and Rudich) imply randomized learning and compression algorithms. This is the first such implication outside of the derandomization ... more >>>

TR15-148 | 9th September 2015
Marco Carmosino, Jiawei Gao, Russell Impagliazzo, Ivan Mikhailin, Ramamohan Paturi, Stefan Schneider

Nondeterministic extensions of the Strong Exponential Time Hypothesis and consequences for non-reducibility

Revisions: 1

We introduce the Nondeterministic Strong Exponential Time Hypothesis
(NSETH) as a natural extension of the Strong Exponential Time
Hypothesis (SETH). We show that both refuting and proving
NSETH would have interesting consequences.

In particular we show that disproving NSETH would ... more >>>

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