Construction of very hard functions for multiparty communication complexity

We consider the multiparty communication model de ned 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 nd 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. AMS Subject Classi cation. 68Q15, 68Q85.

• Type: Journal
• Year: 2000
• Where: ITA
• Authors: Ján Manuch
• Keywords: Communications, Hard Function, ITA 2000, Multiparty Communication Model, Nondeterministic Communication Complexity