Probabilistic communication complexity over the reals

Dima Grigoriev

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arXiv · 0710.2732

Probabilistic communication complexity over the reals

Dima Grigoriev

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Abstract

Deterministic and probabilistic communication protocols are introduced in which parties can exchange the values of polynomials (rather than bits in the usual setting). It is established a sharp lower bound $2n$ on the communication complexity of recognizing the $2n$-dimensional orthant, on the other hand the probabilistic communication complexity of its recognizing does not exceed 4. A polyhedron and a union of hyperplanes are constructed in $\RR^{2n}$ for which a lower bound $n/2$ on the probabilistic communication complexity of recognizing each is proved. As a consequence this bound holds also for the EMPTINESS and the KNAPSACK problems.

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BibTeX RIS

Dima Grigoriev. 2007-10-15. Probabilistic communication complexity over the reals. https://arxiv.org/abs/0710.2732

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