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M.A. Fischler, M. Tannenbaum, "Assumptions in the Threshold Synthesis of Symmetric Switching Functions," IEEE Transactions on Computers, vol. 17, no. 3, pp. 273-279, March, 1968.
 
 
BibTex
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@article{ 10.1109/TC.1968.229102,
author = {M.A. Fischler and M. Tannenbaum},
title = {Assumptions in the Threshold Synthesis of Symmetric Switching Functions},
journal ={IEEE Transactions on Computers},
volume = {17},
number = {3},
issn = {0018-9340},
year = {1968},
pages = {273-279},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1968.229102},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
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TY - JOUR
JO - IEEE Transactions on Computers
TI - Assumptions in the Threshold Synthesis of Symmetric Switching Functions
IS - 3
SN - 0018-9340
SP273
EP279
EPD - 273-279
A1 - M.A. Fischler,
A1 - M. Tannenbaum,
PY - 1968
KW - Index terms?Bounds on complexity
KW - optimal synthesis
KW - symmetric metric functions
KW - symmetric switching circuits
KW - threshold logic.
VL - 17
JA - IEEE Transactions on Computers
ER -
 
Abstract?This note establishes the fact that an optimal synthesis technique (even for a small number of variables) must abandon the basic assumption of assigning only +1 weights to the primary inputs. Examples are presented where both negative primary weights and/or nonunitary primary weights are required to achieve minimality. A method of network analysis is presented which leads to optimal synthesis in a significant number of new cases. The previously accepted lower bound on the number of devices needed to realize a symmetric function is questioned, and a proof is given to establish its validity. A previously published assertion about a least upper bound on the number of devices is shown to be incorrect.
Index Terms:
Index terms?Bounds on complexity, optimal synthesis, symmetric metric functions, symmetric switching circuits, threshold logic.
Citation:
M.A. Fischler, M. Tannenbaum, "Assumptions in the Threshold Synthesis of Symmetric Switching Functions," IEEE Transactions on Computers, vol. 17, no. 3, pp. 273-279, March 1968, doi:10.1109/TC.1968.229102
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