A separation between reconfigurable mesh models

The author proves separations between two models of the reconfigurable mesh (rmesh), the cross-over model and the non-cross-over model. Specifically he shows that in the non-cross-over model, a k ×n rmesh requires Ω((log n)/k) time to compute the parity of n bits stored one per column, and a √n×√n rmesh requires Ω(log*n) time to compute the parity of n bits stored one per processor. In the cross-over model, in either case, the parity can be computed in constant time. The lower bounds given in this paper are the first separations demonstrated between the cross-over and non-cross-over model. These lower bounds do not rely on the bandwidth constraints of the mesh and do not restrict the instruction sets of the processors. Moreover, they are the first lower bounds for the rmesh which require only binary inputs