Lower bounds for VLSI

Increased use of Very Large Scale Integration (VLSI) for the fabrication of digital circuits has led to increased interest in complexity results on the inherent VLSI difficulty of various problems. Lower bounds have been obtained for problems such as integer multiplication (1,2), matrix multiplication [7], sorting [8], and discrete Fourier transform [9], all within VLSI models similar to one originally developed by Thompson [8.9]. The lower bound results all pertain to a space-time trade-off measure that arises naturally within this model. In particular, for all the problems listed above, the results show that if A is the area used by a VLSI circuit to compute one of the n-input, n-output functions listed above, and T is the time required for the computation, then the bound.