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A possible solution to the halting problem

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After watching this video the conclusion may be the following:

  1. Contradictions are a problem in math.

  1. These contradictions seemed to be caused by "self-references".

A possible solution to these problems are to:

  1. Detect self-references.

  1. Illiminate the self-references or break/solve the self-references.

So for example if the H machine is capable of reducing H+ such that H can detect itself inside H+ then this means:

  1. Self reference detected.
  2. Possibly contradiction detected.

Now H can try and work out a solution to this problem/contradiction.

  1. Basically this could allow H to detect H+ enters an infiniteloop, because H has detected itself inside H+, H knows the real answer to the halting question.

So the output of H+ is no longer relevant ! And can be dismissed as a joke/trojan/thruth manipulator.

H detected the real thruth by detecting itself ! HAHA.

So if H can detect halt or infinity then it will no longer be tricked by any machine H+ incorporating itself H.

So this reduces the halting problem/question to:

Can H detect itself given any program/version of itself ! ;)

A reduction problem it seems.

Goodbye for now, Skybuck.

Reply to
skybuck2000
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Get yourself a copy of a book entitled "Gödel, Escher, Bach: an Eternal Golden Braid" by Douglas Hofstadter. It has a very interesting exposition on this whole topic. It's a quirky sort of work to read, but I think it's worth the effort.

The "halting problem" is just one aspect of a much larger problem involving computability and decidability.

The "halting problem" isn't considered solved, unless the analysis program is capable of correctly analysing _any_ working program, and saying "yes, it halts" or "no, it does not halt".

Your solution doesn't do this. If it were implemented (and I'm not at all sure that it is implementable) it would result in an analysis program which has three possible outputs:

(1) "Yes, the program under consideration will halt when fed the input in question." (2) "No, the program under consideration will not halt when fed the input in question." (3) "I refuse to try to answer that question, because the program under consideration looks too much like me."

Answer 3 would be considered a cop-out. You can perhaps keep the analyzer from getting stuck in a contradiction, but this means that it cannot give correct answers to all sets of input.

And this reduction gets you right back to where you started. Can program H, when fed H+, be guaranteed to answer the question "Do I appear inside H+?" correctly in any finite amount of time?

Or, phrasing it another way - is there a program "H-safe?" which can be fed H and H+, and decide (yes or no) whether H is embedded inside H+?

If so, what happens if you feed H-safe? a copy of H-safe? and H?

The problem of detecting self-references is a pervasive and tricky one... it's not as easy to get rid of as your idea suggests. You just end up moving the self-reference problem "one level up" and it comes back.

Reply to
Dave Platt

No you're wrong.

Step 1. Split the program in detecting H and H+.

Analyze H and H+ seperately.

Alan lived during a time of war, any war arguments are valid, to counter his war arguments.

I wasn't looking for your post, but the logic equivalence post of somebody else.

Again also take time and order into account.

My first capture H, if H can prevent capture because of self-awareness, H+ cannot even be build.

Second argument against halting problem.

Bye, Skybuck.

Reply to
skybuck2000

Let's put this argument to rest once and for all:

  1. Skybuck builds Machine H.
  2. Alan captures Machine H.
  3. Alan builds Machine H+ around machine H.
  4. Alan feeds Machine H+ into itself.
  5. Skybuck's Machine H detects Machine H inside Machine H+.
  6. Skybuck's Machine H detects parasite code of Machine H+.
  7. Skybuck's Machine H isolates parasite code of Machine H+.
  8. Skybuck's Machine H analyzes parasite code of Machine H+.
  9. Skybuck's Machine H outputs result for parasite code.

Bye, Skybuck.

Reply to
skybuck2000

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