Abstract
In this work, we continue the research started in [6], 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-talki.e. The motivation for such a communication model comes from the study of the KRW conjecture. Following the open questions formulated in [6], we prove lower bounds for the disjointness function in all variants of half-duplex models and an upper bound in the half-duplex model with zero, that separates disjointness from the inner product function in this setting. Next, we prove lower and upper bounds on the half-duplex complexity of the Karchmer-Wigderson games for the counting functions and for the recursive majority function, adapting the ideas used in the classical communication complexity. Finally, we define the non-deterministic half-duplex complexity and establish bounds connecting it with non-deterministic complexity in the classical model.
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Notes
- 1.
In the original paper, this type of rounds is called spent.
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Dementiev, Y., Ignatiev, A., Sidelnik, V., Smal, A., Ushakov, M. (2021). New Bounds on the Half-Duplex Communication Complexity. In: Bureš, T., et al. SOFSEM 2021: Theory and Practice of Computer Science. SOFSEM 2021. Lecture Notes in Computer Science(), vol 12607. Springer, Cham. https://doi.org/10.1007/978-3-030-67731-2_17
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