Probabilistic Communication Complexity Over The Reals
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A sharp lower bound 2n on the communication complexity of recognizing the 2n-dimensional orthant is established and this bound holds also for the EMPTINESS and the KNAPSACK problems.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 problemsread more
Citations
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Journal Article
Interpolation by a Game
TL;DR: The main objective is to extend the communication complexity approach of 4, 5 to a wider class of proof systems and obtain an eeective interpolation in a form of a protocol of small real communication complexity.
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A Lower Bound for Randomized Algebraic Decision Trees
TL;DR: In this paper, the authors extend the lower bounds on the depth of algebraic decision trees to the case of randomized decision trees with two-sided error for languages being finite unions of hyperplanes and the intersections of halfspaces.
BookDOI
Fundamentals of Computation Theory
Gabriel Ciobanu,Gheorghe Paun +1 more
TL;DR: First nontrivial, in fact quadratic, randomized lower bounds on the problems like Knapsack and Bounded Integer Programming are derived.
Book ChapterDOI
Distributed Algorithmic Mechanism Design and Algebraic Communication Complexity
Markus Bläser,Elias Vicari +1 more
TL;DR: A general algebraic model is defined, where the involved functions can be computed with the natural operations additions, multiplications and divisions and possibly with comparisons, and various lower bound techniques are provided, mainly for fields of characteristic 0.
References
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Book
Communication Complexity
Eyal Kushilevitz,Noam Nisan +1 more
TL;DR: This chapter surveys the theory of two-party communication complexity and presents results regarding the following models of computation: • Finite automata • Turing machines • Decision trees • Ordered binary decision diagrams • VLSI chips • Networks of threshold gates.
Book
Complexity and Real Computation
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Proceedings ArticleDOI
Some complexity questions related to distributive computing(Preliminary Report)
TL;DR: The quantity of interest, which measures the information exchange necessary for computing f, is the minimum number of bits exchanged in any algorithm.
Journal ArticleDOI
Solving systems of polynomial inequalities in subexponential time
TL;DR: The algorithm constructs a certain finite set of solutions for the family of components of connectivity of the set of all real solutions of the system in the case of a positive answer.