Meera Sitharam

We develop an analytic framework based on

linear approximation and point out how a number of complexity

related questions --

on circuit and communication

complexity lower bounds, as well as

pseudorandomness, learnability, and general combinatorics

of Boolean functions --

fit neatly into this framework. ...
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Per Enflo, Meera Sitharam

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Scalar product estimates have so far been used in

proving several unweighted threshold lower bounds.

We show that if a basis set of Boolean functions satisfies

certain weak stability conditions, then

scalar product estimates

yield lower bounds for the size of weighted thresholds

of these basis functions.

Stable ...
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Stasys Jukna

Many dynamic programming algorithms for discrete optimization problems are "pure" in that they only use min/max and addition operations in their recursions. Some of them, in particular those for various shortest path problems, are even "incremental" in that one of the inputs to the addition operations is a variable. We ... more >>>

Shafi Goldwasser, Guy Rothblum, Jonathan Shafer, Amir Yehudayoff

We consider the following question: using a source of labeled data and interaction with an untrusted prover, what is the complexity of verifying that a given hypothesis is "approximately correct"? We study interactive proof systems for PAC verification, where a verifier that interacts with a prover is required to accept ... more >>>

Lijie Chen, Zhenjian Lu, Xin Lyu, Igor Carboni Oliveira

We develop a general framework that characterizes strong average-case lower bounds against circuit classes $\mathcal{C}$ contained in $\mathrm{NC}^1$, such as $\mathrm{AC}^0[\oplus]$ and $\mathrm{ACC}^0$. We apply this framework to show:

- Generic seed reduction: Pseudorandom generators (PRGs) against $\mathcal{C}$ of seed length $\leq n -1$ and error $\varepsilon(n) = n^{-\omega(1)}$ can ... more >>>