Circuits with arbitrary gates for random operators

We consider boolean circuits computing n-operators f : {0, 1}n {0, 1}n . As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes a matrix-vector product Ax over GF(2). We prove the existence of n-operators requiring about n2 wires in any circuit, and linear n-operators requiring about n2 / log n wires in depth2 circuits, if either all output gates or all gates on the middle layer are linear.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Stasys Jukna, Georg Schnitger
• Keywords: Arbitrary Boolean Functions, CORR 2010, Education, Linear, Matrix-vector Product Ax