Entropy
kohmoto
zbi74583 at boat.zero.ad.jp
Sat Apr 2 07:55:29 CEST 2005
Hello, Seqfans.
I have an idea which represents a scale for "Intelligence"of an
algorithm.
I think that it is a kind of "Entropy".
Definition of E(a) :
If a=algorithm
E(a)=1-log{search area of a}/log{object of a}
Example1: Prime test
Divide N by k , k=0 to N^(1/2)
E(P)=1-log(N^(1/2)/logN=1-1/2=0.5
Example2 : Polynomial time prime test
E(PP)=1-log(k*logN)/logN=almost{1-logk/logN}....it depends on k
Example3: x^3+y^3+z^3+u^3=0
E(3rd)=1-log(N^2)/log(N^4)=0.5
Example4: ax^2+bx+c=0
Calculate (-b+(b^2-4ac)^(1/2))/2a .... the search area is only one
point
E(2nd)=1-log1/logN=1
Example5 : Unitary Amicable pair's record.
It has 317 digits.
I searched 10^8 candidates.
E(UA)=1-8/317=0.975
Do Mathematicians know it?
Or, is this scale not so good?
Yasutoshi
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