Nearest neighbor representations of Boolean functions

A nearest neighbor representation of a Boolean function is set positive and negative prototypes in Rn such that the has value 1 on an input iff closest prototype positive. For k-nearest majority classification k considered. The complexity minimal number needed to represent function. We give several bounds for this measure. Separations are given between cases when can be real or required Boolean. parity determined exactly. An exponential lower bound mod 2 inner product, linear its complexity. results proven using connections other models as polynomial threshold functions over {1,2}. also discuss some many open problems arising.