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TR20-118 | 5th August 2020
Oded Goldreich

On Testing Asymmetry in the Bounded Degree Graph Model

We consider the problem of testing asymmetry in the bounded-degree graph model, where a graph is called asymmetric if the identity permutation is its only automorphism. Seeking to determine the query complexity of this testing problem, we provide partial results. Considering the special case of $n$-vertex graphs with connected components ... more >>>

TR20-117 | 4th August 2020
Yuriy Dementiev, Artur Ignatiev, Vyacheslav Sidelnik, Alexander Smal, Mikhail Ushakov

New bounds on the half-duplex communication complexity

In this work, we continue the research started in [HIMS18], where the authors suggested to study the half-duplex communication complexity. Unlike the classical model of communication complexity introduced by Yao, in the half-duplex model, Alice and Bob can speak or listen simultaneously, as if they were talking using a walkie-talkie. ... more >>>

TR20-116 | 1st August 2020
Ivan Mihajlin, Alexander Smal

Toward better depth lower bounds: the XOR-KRW conjecture

In this paper, we propose a new conjecture, the XOR-KRW conjecture, which is a relaxation of the Karchmer-Raz-Wigderson conjecture [KRW95]. This relaxation is still strong enough to imply $\mathbf{P} \not\subseteq \mathbf{NC}^1$ if proven. We also present a weaker version of this conjecture that might be used for breaking $n^3$ lower ... more >>>

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