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Electronic Colloquium on Computational Complexity

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TR23-194 | 5th December 2023
Siddharth Iyer, Anup Rao

XOR Lemmas for Communication via Marginal Information

We define the marginal information of a communication protocol, and use it to prove XOR lemmas for communication complexity. We show that if every $C$-bit protocol has bounded advantage for computing a Boolean function $f$, then every $\tilde \Omega(C \sqrt{n})$-bit protocol has advantage $\exp(-\Omega(n))$ for computing the $n$-fold xor $f^{\oplus ... more >>>

TR23-193 | 3rd December 2023
Eldon Chung, Alexander Golovnev, Zeyong Li, Maciej Obremski, Sidhant Saraogi, Noah Stephens-Davidowitz

On the randomized complexity of range avoidance, with applications to cryptography and metacomplexity

We study the Range Avoidance Problem (Avoid), in which the input is an expanding circuit $C : \{0,1\}^n \to \{0,1\}^{n+1}$, and the goal is to find a $y \in \{0,1\}^{n+1}$ that is not in the image of $C$. We are interested in the randomized complexity of this problem, i.e., in ... more >>>

TR23-192 | 28th November 2023
Noam Mazor, Rafael Pass

A Note On the Universality of Black-box MKtP Solvers

Revisions: 1

The relationships between various meta-complexity problems are not well understood in the worst-case regime, including whether the search version is harder than the decision version, whether the hardness scales with the ``threshold", and how the hardness of different meta-complexity problems relate to one another, and to the task of function ... more >>>

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