View Single Post
  #9  
Old 10-08-2012, 09:49 PM
yaser's Avatar
yaser yaser is offline
Caltech
 
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,477
Default Re: Confused on question 6.

Quote:
Originally Posted by apank View Post
Hi,
What's a possible target function? Is that a combination of boolean operators? How do you come up with the formula 2^2^3 for total number of possibl target functions for 3 boollean inputs? Thank you.
A possible target function is any function that could have generated the 5 data points in this problem, i.e., any function whose values on these five points all agree with the data.

There are 2^3=8 points in the input space here, which are all binary combinations of the 3 input variables from 000 to 111. For each of these points, a Boolean function may return 0 or 1; hence two possibilities. Therefore, for all 8 points, a Boolean function may return 2\times 2 \times \cdots \times 2 (8 times) possibilities, which gives us the number of different Boolean functions 2^{2^3}=2^8=256.
__________________
Where everyone thinks alike, no one thinks very much
Reply With Quote