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Construction of Very Hard Functions for Multiparty Communication Complexity

Published online by Cambridge University Press:  15 April 2002

Ján Maňuch
Ján Maňuch*
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; (manuch@cs.utu.fi)
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Abstract

We consider the multiparty communication model defined in [4] using the formalism from [8]. First, we correct an inaccuracy in the proof of the fundamental result of [6] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nondeterministic communication complexity. The problem to find a particular very hard function was proposed in [7], where it has been shown that almost all functions are very hard. We also prove that combining two very hard functions by the Boolean operation xor gives a very hard function.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 1 , January 2000, pp. 61 - 75
Copyright
© EDP Sciences, 2000

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