The Realization of Symmetric Switching Functions with Linear-Input Logical Elements
- 1 September 1961
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Electronic Computers
- Vol. EC-10 (3) , 371-378
- https://doi.org/10.1109/tec.1961.5219224
Abstract
The problem of synthesizing switching networks out of linear-input (threshold) elements is studied for the class of symmetric switching functions. Tight bounds are derived for the number of elements required in a minimal realization, and a method of synthesis is presented which yields economical networks. Minimal networks result for all symmetric functions of no more than about twelve variables, and for several other cases. In particular, it is shown how the parity function of any number n of variables can be realized with about log2(n) elements.Keywords
This publication has 4 references indexed in Scilit:
- Unate Truth FunctionsIEEE Transactions on Electronic Computers, 1961
- Linear-Input LogicIEEE Transactions on Electronic Computers, 1961
- On the Inversion Complexity of a System of FunctionsJournal of the ACM, 1958
- A symbolic analysis of relay and switching circuitsTransactions of the American Institute of Electrical Engineers, 1938