Beefy Boxes and Bandwidth Generously Provided by pair Networks
There's more than one way to do things

Re^2: Boolean math: Fill in the blanks.

by BrowserUk (Pope)
on Oct 12, 2008 at 08:25 UTC ( #716662=note: print w/replies, xml ) Need Help??

in reply to Re: Boolean math: Fill in the blanks.
in thread Boolean math: Fill in the blanks.

Conclusion: ... I see some inconsistent results ... 7 of ( R & R | R & R ) & R evaluates to 5 bits set on average.

If you plug ( R & R | R & R ) & R into the OP code and run it a few times, you'll see that the average does approximate 7:

C:\test>booleanBuk -N=1e2 7.02 C:\test>booleanBuk -N=1e2 6.88 C:\test>booleanBuk -N=1e2 7.06 C:\test>booleanBuk -N=1e2 7.06 C:\test>booleanBuk -N=1e2 6.92 C:\test>booleanBuk -N=1e2 7.08

And as you increase the number of iterations, the more closely the observations coincide with the theoretical value:

C:\test>booleanBuk -N=1e5 7.00138 C:\test>booleanBuk -N=1e5 6.98986 C:\test>booleanBuk -N=1e5 6.99812 C:\test>booleanBuk -N=1e5 7.00729 C:\test>booleanBuk -N=1e6 6.994402 C:\test>booleanBuk -N=1e6 7.002038

That's how I like my proofs. Tangible :)

Sorry if I have misunderstood your hypothesis.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

Replies are listed 'Best First'.
Re^3: Boolean math: Fill in the blanks.
by repellent (Priest) on Oct 12, 2008 at 16:54 UTC
    But plug in
      (( R & R ) | R ) & R & R

    into the OP code and it tends towards 5, which was how I was interpreting the expression:
      ( R & R | R & R ) & R

    My mistake. Perl evaluates ( R & R | R & R ) & R as ( (R & R) | (R & R) ) & R and that, according to my hypothesis, results in 7 bits set on average.

Log In?

What's my password?
Create A New User
Node Status?
node history
Node Type: note [id://716662]
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others meditating upon the Monastery: (5)
As of 2016-10-25 05:24 GMT
Find Nodes?
    Voting Booth?
    How many different varieties (color, size, etc) of socks do you have in your sock drawer?

    Results (315 votes). Check out past polls.