Separating NOF communication complexity classes RP and NP

In the number-on-forehead (NOF) model of communication complexity, k players are trying to evaluate a function F defined on kn bits. The input of F is partitioned into k pieces of n bits each, call them x1, . . . ,xk, and xi is placed, metaphorically, on the forehead of player i. Thus, each player sees (k − 1)n of the kn input bits. The players communicate by writing bits on a shared blackboard in order to compute F . This model was introduced by [5] and it has many applications, including circuit lower bounds [9, 11], time/space tradeoffs for Turing Machines, pseudo-random number generators for space-bounded Turing Machines [2], and proof system lower bounds [4].