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