Building logic gates with perceptrons

Computer Science Level pending

In this problem, we saw that perceptrons can indeed be used to model logic gates.

How many boolean function in 2 variables are there that can be modelled using a single perceptron?


The answer is 14.

Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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1 solution

展豪 張
Aug 26, 2016

The only two boolean functions which could not be modeled are XOR and NXOR.

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That's correct. Can you try explaining why?

Agnishom Chattopadhyay - 4 years, 9 months ago

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Sure! If you plot the inputs into a graph, you will find that seeking for a single perceptron trying to model the XOR or NXOR is like finding a way to draw a line such that two opposite corners of a square are on one side and the other two on the other side, which is impossible. These data set is called non linear separable.

展豪 張 - 4 years, 9 months ago

single perceptron can only model functions whose graphical models are linearly separable. So, if there is no line (or plane, or hyperplane, etc. depending on the number of dimensions) that divides the fires and the non-fires (the pluses and minuses), then it isn't possible for the perceptron to learn to behave with that pattern of firing. For instance, the boolean function XOR is not linearly separable, so you can't model this boolean function with only one perceptron.

Hasmik Garyaka - 3 years, 7 months ago

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