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Electronic Colloquium on Computational Complexity

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TR22-108 | 18th July 2022
Shuichi Hirahara, Nobutaka Shimizu

Hardness Self-Amplification from Feasible Hard-Core Sets

We consider the question of hardness self-amplification: Given a Boolean function $f$ that is hard to compute on a $o(1)$-fraction of inputs drawn from some distribution, can we prove that $f$ is hard to compute on a $(\frac{1}{2} - o(1))$-fraction of inputs drawn from the same distribution? We prove hardness ... more >>>


TR22-107 | 20th July 2022
Shachar Lovett, Jiapeng Zhang

Fractional certificates for bounded functions

A folklore conjecture in quantum computing is that the acceptance probability of a quantum query algorithm can be approximated by a classical decision tree, with only a polynomial increase in the number of queries. Motivated by this conjecture, Aaronson and Ambainis (Theory of Computing, 2014) conjectured that this should hold ... more >>>


TR22-106 | 21st July 2022
Suryajith Chillara, Coral Grichener, Amir Shpilka

On Hardness of Testing Equivalence to Sparse Polynomials Under Shifts

We say that two given polynomials $f, g \in R[x_1, \ldots, x_n]$, over a ring $R$, are equivalent under shifts if there exists a vector $(a_1, \ldots, a_n)\in R^n$ such that $f(x_1+a_1, \ldots, x_n+a_n) = g(x_1, \ldots, x_n)$. This is a special variant of the polynomial projection problem in Algebraic ... more >>>



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