Recurrent Ultracomputers are not log N-Fast by

Ultracomputers are assemblages of processors that are able to operate concurrently and can exchange data through communication lines in, say, one cycle of operation. For physical reasons, the fan in/out of the processors must be limited. This imposes restric-tions on the possible communication schemes. I to have the ultracomputer operate efficiently as a whole, it is desirable that arbitrary exchanges of information between the processors can be effected in small number of data shifts. If a really huge ultracomputer is built, it would be nice if it could be constructed by coupling smaller ultracomputers, which in turn are assembled from still smaller ultra-computers, and so on. It will be shown that the latter desire conflicts to a certain extent with the earlier one. 1