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K.N. Levitt, "R7038 The Time Required for Group Multiplication," IEEE Transactions on Computers, vol. 19, no. 9, pp. 859860, September, 1970.  
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@article{ 10.1109/TC.1970.223066, author = {K.N. Levitt}, title = {R7038 The Time Required for Group Multiplication}, journal ={IEEE Transactions on Computers}, volume = {19}, number = {9}, issn = {00189340}, year = {1970}, pages = {859860}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1970.223066}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  R7038 The Time Required for Group Multiplication IS  9 SN  00189340 SP859 EP860 EPD  859860 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 rinput, singleoutput modules, with each inputoutput 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 11 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, "R7038 The Time Required for Group Multiplication," IEEE Transactions on Computers, vol. 19, no. 9, pp. 859860, Sept. 1970, doi:10.1109/TC.1970.223066
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