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

Probabilistic communication complexity over the reals