Weakening Cycles So That Turing Can Halt
The article uses an intuitive approach trying to find a way to crack the halting problem.<p>But the truth is that halting dilemma is real and despite any attempt to &quot;unwind&quot; or &quot;simplify&quot; the control and data flows, there is a real barrier. It is in the math.<p>My favorite example: finding an odd perfect number. Euler stated: &quot;Whether (...) there are any odd perfect numbers is a most difficult question&quot;. More recently, Carl Pomerance has presented a heuristic argument suggesting that indeed no odd perfect number should exist. [1]<p>Does it exist? Definitely. Somewhere in 10^300 range. What is the exact value? Nobody knows. You can write a program that finds an odd perfect number:<p><pre><code>    def odd_perfect_number():
        n = 1
        while True:
            if sum(filter(lambda x: n % x == 0, xrange(1, n))) == n:
                return &quot;OK! I FIND IT!&quot;
            n += 2
</code></pre>
Will this program ever complete?<p>Maybe. However nobody can say for sure. Avoiding recursion or some kind of groups won&#x27;t give you any favor.<p>This is the halting problem in all of its glory.<p>[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Perfect_number" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Perfect_number</a>