
Analysis of Boolean Functions - luu
http://www.contrib.andrew.cmu.edu/~ryanod/
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amathstudent
I was wondering: I find this topic interesting from a conceptual point of
view, but I'm reluctant to learn more about it without having some concrete
useful application as motivation. Can anyone give an example like that?

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chaoxu
As far as I know, the applications are for theoretical problems and has no
application in everyday work.

~~~
amathstudent
That's fine, I like theoretical problems too.

~~~
chaoxu
For cs people the more important would be property testing, since often we are
interested in finding out if something holds with high probability without
read everything. A common possibility is mapping a subset of set of vertices
of a graph to a boolean. say, is the subset of vertices a independent set.

The simplest example would be testing how close f is to a linear function.

We consider f:{0,1}^n->{0,1}. f is linear if f(x+y)=f(x)+f(y), and there are
different ways to measure almost linearity. Either the probability that
randomly picking x and y, we have f(x+y)=f(x)+f(y), the other would be how far
away the function is from a linear function in hamming distance.

Using the tools in analysis of boolean functions, we can show these two
measures are basically the same.

[http://www.contrib.andrew.cmu.edu/~ryanod/?p=279](http://www.contrib.andrew.cmu.edu/~ryanod/?p=279)

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coin
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