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S. Kundu, "Basis Sets for Synthesis of Switching Functions," IEEE Transactions on Computers, vol. 41, no. 4, pp. 489493, April, 1992.  
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@article{ 10.1109/12.135561, author = {S. Kundu}, title = {Basis Sets for Synthesis of Switching Functions}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {4}, issn = {00189340}, year = {1992}, pages = {489493}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.135561}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Basis Sets for Synthesis of Switching Functions IS  4 SN  00189340 SP489 EP493 EPD  489493 A1  S. Kundu, PY  1992 KW  synthesis; switching function; completeness; basis set; logic primitives; ReedMuller expansion; logic design; switching functions. VL  41 JA  IEEE Transactions on Computers ER   
The synthesis of switching function f(x/sub 1/, x/sub 2/, . . ., x/sub n/) from a given family of functions g/sub i/(x/sub 1/, x/sub 2/, . . ., x/sub n/), 1>or=i>or=k, using a complete set of logic primitives is considered. Necessary and sufficient conditions for the synthesis of f from the g/sub i/'s are derived using the concept of a basis set. The independence between the basis property and the completeness of a set of logic primitives is shown, the conditions for extending a set (g/sub 1/, g/sub 2/, . . ., g/sub j/), j>n, to a basis set are found. Thus, the selection of a basis set and the logic primitives can be treated as separate problems. Finally, it is shown that there is a unique generalized ReedMuller expansion for any f in terms of the basis functions (g/sub i/).
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