On communication complexity of vector-valued functions

New upper and lower bounds on the two-way communication complexity of abstract functions g:ℋ×𝒴→𝒵 give tight bounds, when applied to vector-valued functions fⁿ(f₁ ,...,f_n):ℋ^u×𝒴ⁿ →𝒵ⁿ, if the alphabets are small. For the set-intersection function, an optimal protocol is presented. It is based on a simple new idea applicable also to abstract functions. The two-way communication complexities of all other Boolean functions are also determined. The results are extended to meets in abstract lattices and to a probabilistic model