Russell Impagliazzo, Shachar Lovett, Ramamohan Paturi, Stefan Schneider

We give an exact algorithm for the 0-1 Integer Linear Programming problem with a linear number of constraints that improves over exhaustive search by an exponential factor. Specifically, our algorithm runs in time $2^{(1-\text{poly}(1/c))n}$ where $n$ is the

number of variables and $cn$ is the number of constraints. The key ...
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Takayuki Sakai, Kazuhisa Seto, Suguru Tamaki, Junichi Teruyama

In this paper, we present a moderately exponential time algorithm for the circuit satisfiability problem of

depth-2 unbounded-fan-in circuits with an arbitrary symmetric gate at the top and AND gates at the bottom.

As a special case, we obtain an algorithm for the maximum satisfiability problem that runs in ...
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Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Pierre McKenzie, Shadab Romani

The Black-Box Hypothesis, introduced by Barak et al. (JACM, 2012), states that any property of boolean functions decided efficiently (e.g., in BPP) with inputs represented by circuits can also be decided efficiently in the black-box setting, where an algorithm is given an oracle access to the input function and an ... more >>>

Swapnam Bajpai, Vaibhav Krishan, Deepanshu Kush, Nutan Limaye, Srikanth Srinivasan

We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to $C$ in significantly better than ... more >>>

Ryan Williams

Many results in fine-grained complexity reveal intriguing consequences from solving various SAT problems even slightly faster than exhaustive search. We prove a ``self-improving'' (or ``bootstrapping'') theorem for Circuit-SAT, $\#$Circuit-SAT, and its fully-quantified version: solving one of these problems faster for ``large'' circuit sizes implies a significant speed-up for ``smaller'' circuit ... more >>>