On 03/06/2024 01:16, immibis wrote:
The halting problem says you can't find a Turing machine that tells whether executing each other Turing machine will halt. Simulation has nothing to do with the question.
Background:
PO claims to have refuted the common HP proof, e.g. as covered in the Linz book "An Introduction to Formal Languages and Automata". PO occasionally posts a link to a PDF containing an extract of the 5 or so pages of the book containing the proof, but I expect you have access to this or equivalent.
In a nutshell, the proof goes:
- Suppose H is a TM Halt decider that decides for any input <P><I> whether
TM P run with input I on its input tape halts.
[<P> is the string representation of the actual TM P, and
<I> is the string representation of input tape I]
- Construct from H a new TM H^ using the mechanical process described in the proof.
If H exists, then its corresponding H^ also exists.
- Show that the construction of H^ ensures that:
- if H decides input <H^><H^> (representing H^ running with input <H^>) halts,
then that implies that H^ running with input <H^> never halts
- if H decides input <H^><H^> never halts,
then that implies H^ running with input <H^> halts
I.e. either way, H decides the specific input <H^><H^> incorrectly, contradicting
the initial assumption that H is a halt decider.
- So no halt decider exists. (Every proposed halt decider decides at least one input case
incorrectly, viz input <H^><H^>.)
PO basically claimed he had a fully coded TM H, which CORRECTLY decides its "nemesis" input <H^><H^>, contradicting the logic of the Linz proof [without pointing out any actual mistake in the Linz proof]. Given most people here understand the Linz proof well enough to see it is basically sound, people were sceptical!
It turned out PO was lying about the fully coded TM, and in fact what he actually had was the idea behind a C program which would "prove" his idea. A couple of years(?) later he actually completed his C program and his x86utm.exe which would simulate the x86 code of his H and H^ to "prove" his claim. His equivalent of Linz H is his C function H or HH, and his equivalent of Linz H^ is his D or DD respectively. (They run under x86utm.exe and are not Windows/Unix executables.)
H/HH use PARTIAL simulation of their input to decide halting/non-halting, returning
0 or 1 to communicate their decision. As you correctly point out, to the HP proof simulation is quite irrelevant, being just one kind of data manipulation that H may perform on its input string <P><I> before it decides the halting status. So the Linz HP proof covers such H, no problem.
[I put PARTIAL in caps, just because there seems to be some confusion in recent threads as to what PO means by "simulation". He doesn't say it explicitly, despite suggestions to this effect, but he always means what might be called /partial/ simulation.]
PO believes that by (partially) simulating the computation corresponding to the input <P><I> [i.e. calculating the successive x86 instruction steps of the computation P(I)] and monitoring the progress of virtual x86 state changes (like instruction address and op-code and so on) H could spot some pattern that reveals whether computation P(I) halts or not. At this point in the partial simulation, his H would stop simulating (aka "abort" the simulation) and return the appropriate halt status for input <P><I>.
Nothing remarkable so far! Clearly a tight-loop in P /can/ be detected in this fashion, so /some/ <P><I> inputs /can/ be correctly determined like this. The PO claim however is that the specific input <H^><H^> is correctly decided by his H. In C terms those correspond to H(D,D) correctly returning the halt status of computation D(D). [PO would probably dispute this, because he doesn't properly understand halting or the HP generally, or in fact pretty much /any abstract concept/ ]
So of great interest in all this would be: what in fact is the halt status of PO's contoversial D(D), and what in fact does his H(D,D) return as the halt status of that input, right?
PO's D(D) halts, as illustrated in various traces that have been posted here.
PO's H(D,D) returns 0 : [NOT halting] also as illustrated in various traces.
i.e. exactly as the Linz proof claims. PO has acknowledged both these results. Same for the HH/DD variants.
You might imagine that's the end of the matter - PO failed. :)
That's right, but PO just carries on anyway! Where 99.99% students would think "damn, where did I go wrong" and go back over their thinking to identify their mistake [aka "learn" from the whole episode], PO just doubles down on his original claim, modifying it to [something barely coherent and clearly not refuting any HP proof]. I can't even bring myself to try to explain exactly what PO claims these days. IT DOES NOT MATTER unless you really feel a need to "understand" PO and where he goes wrong.
And while we're here, "arguing" with PO about anything is also pointless :) in so far that:
- PO is /unable/ to understand your arguments or even the definition of the
terms you use. And he is incapable of logically explaining his own position.
In the end he just believes what he thinks is right (his intuitions) regardless
of any "logic" aka "extraneous complexity" that responders employ! I put this down
to some physical brain-wiring issue that PO has, meaning he cannot cope with
abstract concepts like others can. [...but who knows at that level...]
NOTE: it's not that PO isn't concentrating, or that people aren't explaining
clearly enough. I know there's a tendancy for posters to think that the lack of
genuine communication with PO is their fault, or at least something they can address
somehow. It's not.
- So people here can't "help" him by getting him to understand his mistakes - that's
just not going to happen. PO will die firmly believing that he is an
unacknowledged genius with superior powers of concentration/reasoning to all
of us. That may seem UNJUST, but it is unavoidable, and really DOESN'T MATTER;
When PO dies (as everyone dies) the world will just carry on as it does.
- no "innocent student" is going to read PO's claims and think "aha, looks like
the Halting Problem is decideable after all! I'll use that in my exams next week
to gain extra points"! [Or if they do, they'll get what they deserve :)]
People who understand HP quickly figure out PO is just a crank, although it may take some
time for them to see the bigger picture of what PO is claiming etc. if they get that far.
Crankhood can be quickly decided due to PO's constant use of "duffer phrasing"
and general lack of coherency in everything he posts - actual geniuses don't do that.
So really, there's no /need/ to "refute" everything he says - the end result will be exactly the same as just ignoring him, BUT WITH THE LATTER ONLY NEEDING 0.1% OF THE EFFORT and eliminating 99.9% of the posting clutter in these newsgroups. [ok, comp.theory will die pretty quickly, but it is not discussing anything useful, so that's ok for most people... (with some reluctance)]
Mike.
Why does Olcott care about simulation, anyway?
Re: Why does Olcott care about simulation, anyway?
