Probabilistic Communication Complexity Over The Reals

  • Authors:

  • Dima Grigoriev

  • Affiliations:

  • Université de Rennes Beaulieu, CNRS, IRMAR, 35042, Rennes, France

  • Venue:
  • Computational Complexity
  • Year:
  • 2008

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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 recognizing it does not exceed 4. A polyhedron and a union of hyperplanes are constructed in $$\mathbb{R}^{2n}$$for which a lower bound n on the probabilistic communication complexity of recognizing each is proved. As a consequence this bound holds also for the EMPTINESS and the KNAPSACK problems.