Dan Gutfreund

Fooling Parity Tests with Parity Gates

We study the complexity of computing k-wise independent and e-biased generators G : {0, 1} n → {0, 1} m . Specifically, we refer to the complexity of computing Gexplicitly, i.e. given x ∈ {0, 1} n and i ∈ {0, 1}log m computing the i-th output bit of G(x). [MNT90] show that constant depth circuits of size poly(n) cannot explicitly compute k-wise independent and e-biased generators with seed length \(n \leq 2^{\log^{o(1)} m}\).

If NP languages are hard on the worst-case then it is easy to find their hard instances

We prove that if NP /spl nsube/ BPP, i.e., if some NP-complete language is worst-case hard, then for every probabilistic algorithm trying to decide the language, there exists some polynomially samplable distribution that is hard for it. That is, the algorithm often errs on inputs from this distribution. This is the first worst-case to average-case reduction for NP of any kind. We stress however, that this does not mean that there exists one fixed samplable distribution that is hard for all probabilistic polynomial time algorithms, which is a pre-requisite assumption needed for OWF and cryptography (even if not a sufficient assumption). Nevertheless, we do show that there is a fixed distribution on instances of NP-complete languages, that is samplable in quasi-polynomial time and is hard for all probabilistic polynomial time algorithms (unless NP is easy in the worst-case). Our results are based on the following lemma that may be of independent interest: Given the description of an efficient (probabilistic) algorithm that fails to solve SAT in the worst-case, we can efficiently generate at most three Boolean formulas (of increasing lengths) such that the algorithm errs on at least one of them.

A lower bound for testing juntas

We show an Ω(m) lower bound on the number of queries required to test whether a Boolean function depends on at most m out of its n variables. This improves a previously known lower bound for testing this property. Our proof is simple and uses only elementary techniques.

A Benchmark Dataset for Automatic Detection of Claims and Evidence in the Context of Controversial Topics

We describe a novel and unique argumentative structure dataset. This corpus consists of data extracted fro m hundreds of Wikipedia articles using a meticulously monitored manual annotation process. The result is 2,683 argument elements, collected in the context of 33 controversial topics, organized under a simp le claim-evidence structure. The obtained data are publicly available for academic research.

Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games

AbstractImpagliazzo and Wigderson proved a uniform hardness vs. randomness “gap theorem” for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in

A (de)constructive approach to program checking

\textrm{E = DTIME}(2^{O(n)})

If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances

can be proved to a subexponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm such that it is infeasible to come up with inputs on which the algorithm fails. We also show that if Arthur-Merlin protocols are not very strong (in the sense explained above) then