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| - Construction of Very Hard Functions for Multiparty Communication Complexity
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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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