TY - JOUR
T1 - Linear circuits over GF(2)
AU - Alon, Noga
AU - Karchmer, Mauricio
AU - Wigderson, Avi
PY - 1990
Y1 - 1990
N2 - For n = 2k, let S be an n × n matrix whose rows and columns are indexed by GF(2)k and, for i, j member of GF(2)k, Si,j = 〈i,j〉, the standard inner product. Size-depth trade-offs are investigated for computing Sx with circuits using only linear operations. In particular, linear size circuits with depth bounded by the inverse of an Ackerman function are constructed, and it is shown that depth two circuits require Ω(n log n) size. The lower bound applies to any Hadamard matrix.
AB - For n = 2k, let S be an n × n matrix whose rows and columns are indexed by GF(2)k and, for i, j member of GF(2)k, Si,j = 〈i,j〉, the standard inner product. Size-depth trade-offs are investigated for computing Sx with circuits using only linear operations. In particular, linear size circuits with depth bounded by the inverse of an Ackerman function are constructed, and it is shown that depth two circuits require Ω(n log n) size. The lower bound applies to any Hadamard matrix.
UR - http://www.scopus.com/inward/record.url?scp=0025640505&partnerID=8YFLogxK
U2 - 10.1137/0219074
DO - 10.1137/0219074
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AN - SCOPUS:0025640505
SN - 0097-5397
VL - 19
SP - 1064
EP - 1067
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 6
ER -