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E. Kellerman, "A Formula for Logical Network Cost," IEEE Transactions on Computers, vol. 17, no. 9, pp. 881884, September, 1968.  
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@article{ 10.1109/TC.1968.229149, author = {E. Kellerman}, title = {A Formula for Logical Network Cost}, journal ={IEEE Transactions on Computers}, volume = {17}, number = {9}, issn = {00189340}, year = {1968}, pages = {881884}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1968.229149}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  A Formula for Logical Network Cost IS  9 SN  00189340 SP881 EP884 EPD  881884 A1  E. Kellerman, PY  1968 KW  Index Terms?Complexity KW  cost formula KW  logic design KW  Monte Carlo KW  network cost KW  switching circuit cost. VL  17 JA  IEEE Transactions on Computers ER   
Abstract?The cost, or complexity, of a switching network is defined in two ways: by its diode count and by the number of modules from a predefined set required to build it. These modules were chosen as representative of a modular diodetransistor technology. With the aid of Monte Carlo methods the following formula was obtained for the average cost, C(n, g, h), of the twolevel minimal form of a 1output combinational logical network which implements a Boolean function with g "one" vertices, h "zero" vertices, and n independent variables: where the K's are constants. Since the same formula, except for the values of the constants, was obtained for the two different definitions of cost, one hopes that it would only be necessary to change the value of the constants to use the formula with other technologies. The formula was tested on 195 computergenerated samples. The average error was found to be 15.3 percent for the diode count and 15.7 percent for the module count. With the values of the K's set for predicting average diode count, the formula was tested on 48 existing networks. The average percentage error between predicted and actual cost was found to be 32.9 percent (the higher error is possibly due to a nonrandom selection of the input codes).
Index Terms:
Index Terms?Complexity, cost formula, logic design, Monte Carlo, network cost, switching circuit cost.
Citation:
E. Kellerman, "A Formula for Logical Network Cost," IEEE Transactions on Computers, vol. 17, no. 9, pp. 881884, Sept. 1968, doi:10.1109/TC.1968.229149
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