We consider the multiparty communication model defined in [DF89] using the formalism from [Hr97]. First, we correct an inaccuracy in the proof of the fundamental result of [DR95] 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 [Du99], 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.
CITATION STYLE
Maňuch, J. (1999). Multiparty communication complexity: Very hard functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1672, pp. 160–169). Springer Verlag. https://doi.org/10.1007/3-540-48340-3_15
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