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Enumeration of Threshold Functions of Eight Variables
September 1970 (vol. 19 no. 9)
pp. 818-825
| ASCII Text | x | ||
| S. Muroga, T. Tsuboi, C.R. Baugh, "Enumeration of Threshold Functions of Eight Variables," IEEE Transactions on Computers, vol. 19, no. 9, pp. 818-825, September, 1970. | |||
| BibTex | x | ||
| @article{ 10.1109/T-C.1970.223046, author = {S. Muroga and T. Tsuboi and C.R. Baugh}, title = {Enumeration of Threshold Functions of Eight Variables}, journal ={IEEE Transactions on Computers}, volume = {19}, number = {9}, issn = {0018-9340}, year = {1970}, pages = {818-825}, doi = {http://doi.ieeecomputersociety.org/10.1109/T-C.1970.223046}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Enumeration of Threshold Functions of Eight Variables IS - 9 SN - 0018-9340 SP818 EP825 EPD - 818-825 A1 - S. Muroga, A1 - T. Tsuboi, A1 - C.R. Baugh, PY - 1970 KW - Completely monotonic functions KW - enumeration of threshold functions KW - linear programming KW - optimum structure KW - switching theory KW - threshold logic. VL - 19 JA - IEEE Transactions on Computers ER - | |||
The number of threshold functions of eight variables is counted by ILLIAC II, the computer of the University of Illinois. Sets of optimum weights of majority elements realizing these functions also are investigated. Actually, canonical positive self-dual threshold functions of nine variables are investigated instead of directly investigating threshold functions of eight variables because it is easier to deal with them. The number and optimum weights of threshold functions of eight variables are easily obtained from these functions of nine variables and their realization.
Index Terms:
Completely monotonic functions, enumeration of threshold functions, linear programming, optimum structure, switching theory, threshold logic.
Citation:
S. Muroga, T. Tsuboi, C.R. Baugh, "Enumeration of Threshold Functions of Eight Variables," IEEE Transactions on Computers, vol. 19, no. 9, pp. 818-825, Sept. 1970, doi:10.1109/T-C.1970.223046
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