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Consider all functions $f : \{-1, 0, 1\}^3 \to \{-1, 1\}$. How many of these functions exist and how many can be realized by a perceptron.

What are the conditions that one has to check?

N.B. A perceptron is a function $f_{w,b} : {\bf R}^n \to {\bf R}$ such that $f_{w,b}(x) = {\rm sgn}(w\cdot x - b)$

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    @Makholm/Wong - How does one see how many of these possible functions can be realized by a perceptron?2012-07-03

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