Probabilistic communication complexity over the reals

Details Probabilistic communication complexity over the reals Probabilistic communication complexity over the reals

2007-10-15

arxiv.org/abs/0710.2732v1

Computer Science

Computational Complexity

Scientific paper

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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