Abstract
It is shown that quasi-threshold realization of a set of ternary functions is possible, when separating surfaces in the hypercube of a ternary function are allowed to be of second degree. Only one constraint is required to obtain simple physical realizations of these "Polynomial Separable" functions, which considerably outnumber the Linear Separable functions. It is shown that monotonic-transformability is a necessary condition for a ternary function to be polynomial separable. There are 2967 2-place and over 1.5 million 3-place ternary polynomial separable functions. Identifiers and realization parameters have been listed for the 2-place case and for a subset of the 3-place case.
Alexander von Humboldt Research Fellow at the Universität Dortmund, Abteilung Informatik; on leave from: Dept. of Computer Science, University Santa María, Valparaíso, Chile
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6. References
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Moraga, C. (1975). Polynomial separation of ternary functions. In: Mülbacher, J. (eds) GI — 5. Jahrestagung. GI 1975. Lecture Notes in Computer Science, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07410-4_656
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DOI: https://doi.org/10.1007/3-540-07410-4_656
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