The VLSI complexity of Boolean functions
نویسندگان
چکیده
It is well-known that all Boolean functions of n variables can be computed by a logic circuit with o(2n/n) gates (Lupanov's theorem) and that there exist Boolean functions of n variables which require logic circuits of this size (Shannon's theorem). We present corresponding results for Boolean functions computed by VLSI circuits, using Thompson's model of a VLSI chip. We prove that all Boolean functions of n variables can be computed by a VLSI circuit of O (2 n) area and period i, and we prove that there exist Boolean functions of n variables for which every (convex) VLSI chip must have (2 n) area.
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