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| ASCII Text | x | ||
| K.N. Levitt, "R70-38 The Time Required for Group Multiplication," IEEE Transactions on Computers, vol. 19, no. 9, pp. 859-860, September, 1970. | |||
| BibTex | x | ||
| @article{ 10.1109/T-C.1970.223066, author = {K.N. Levitt}, title = {R70-38 The Time Required for Group Multiplication}, journal ={IEEE Transactions on Computers}, volume = {19}, number = {9}, issn = {0018-9340}, year = {1970}, pages = {859-860}, doi = {http://doi.ieeecomputersociety.org/10.1109/T-C.1970.223066}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - R70-38 The Time Required for Group Multiplication IS - 9 SN - 0018-9340 SP859 EP860 EPD - 859-860 A1 - K.N. Levitt, PY - 1970 KW - null VL - 19 JA - IEEE Transactions on Computers ER - | |||
Applying some simple, easily understood principles, Spira, in extending some earlier work of Winograd, points the way to a powerful theory of computation complexity. Spira considers a (d, r) combinational network which is an interconnection of r-input, single-output modules, with each input-output line carrying a value from the set {0, 1, ? , d -1}. A finite function f: X1 ? X2 ? ? Xn?Y is to be computed, but it is assumed that before the inputs are inserted into the network, each input can be individually (and arbitrarily) transformed by a set of maps gj: Xj?Ij. It is also assumed that there is a 1-1 output map h: Y?Oc, so in practice the (d, r) network will have as input [g1(x), ?, gn(xn)] and as output h(f(x1, ?, xn)). The problem is to bound the number of levels required of the network. Given a f for a particular output mapping, it is not difficult to specify a lower bound on the number of levels required, by identifying for each output line the number of different values of input variables which yield a different output value. The minimum number of levels required for each output line is then evaluated by noting that an output at level z can depend on at most r' input lines whence the output line requiring the most levels provides the bound.
Citation:
K.N. Levitt, "R70-38 The Time Required for Group Multiplication," IEEE Transactions on Computers, vol. 19, no. 9, pp. 859-860, Sept. 1970, doi:10.1109/T-C.1970.223066
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