On relations between input and communication/computation in VLSI

Abstract

This extended abstract examines some of the fundamental issues involved. It is shown that when multiple copies of the inputs are allowed the standard methodology for deriving lower bounds on the complexity of VLSI chips is no longer applicable. A simple example is presented whose upper bound complexity with mUltiple copies of the inputs is below the lower bound complexity of that function when only a single copy of the inputs upper and lower bounds on such complexity for certain functions or families of functions. An important assumption made in the cited literature is that the inputs to the computations are made available to the chip only once. While this assumption is not of significance in the context of classical algorithm design for random access machines, it may carry important implications in the context of VLSI, where providing several copies of the inputs may be successfully employed to reduce the complexity of the computation. have is allowed. Finally, lower bounds on the complexity of a family of functions are derived for the case when multiple copies of the inputs are permitted.