Area Time Optimal VLSI Circuits for Convolution
IEEE Transactions on Computers
Computational Geometry on a Systolic Chip
IEEE Transactions on Computers
Two VLSI Structures for the Discrete Fourier Transform
IEEE Transactions on Computers
IEEE Transactions on Computers
Integration, the VLSI Journal
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We introduce a property of boolean functions, called transitivity which holds of integer, polynomial, and matrix products as well as of many interesting related computational problems. We show that the area of any circuit computing a transitive function grows quadratically with the circuit's maximum data-rate, expressed in bit/second. This result provides a precise analytic expression of an area-time tradeoff for a wide class of V.L.S.I. circuits. Furthermore, (as shown elsewhere), this tradeoff is achievable. Thus we have matching (to within a constant multiplicative factor) upper and lower complexity bounds for the three above products, in the V.L.S.I. circuits computational model.