Re: Halting Problem: What Constitutes Pathological Input

On 5/8/25 1:02 AM, olcott wrote:

On 5/7/2025 10:48 PM, Richard Damon wrote:

On 5/7/25 11:15 PM, olcott wrote:

On 5/7/2025 9:09 PM, Richard Damon wrote:

On 5/7/25 11:31 AM, olcott wrote:

On 5/7/2025 5:55 AM, Richard Damon wrote:

On 5/6/25 10:09 PM, olcott wrote:

On 5/6/2025 5:52 PM, Richard Damon wrote:

On 5/6/25 4:37 PM, olcott wrote:

On 5/6/2025 3:22 PM, joes wrote:

Am Tue, 06 May 2025 13:05:15 -0500 schrieb olcott:

On 5/6/2025 5:59 AM, Richard Damon wrote:

On 5/5/25 10:18 PM, olcott wrote:

On 5/5/2025 8:59 PM, dbush wrote:

On 5/5/2025 8:57 PM, olcott wrote:

On 5/5/2025 7:49 PM, dbush wrote:

>

DO COMPUTE THAT THE INPUT IS NON-HALTING IFF (if and only if) the
mapping FROM INPUTS IS COMPUTED.

i.e. it is found to map something other than the above function
which is a contradiction.

The above function VIOLATES COMPUTER SCIENCE. You make no attempt to
show how my claim THAT IT VIOLATES COMPUTER SCIENCE IS INCORRECT you
simply take that same quote from a computer science textbook as the
infallible word-of-God.

What does it violate?
>

All you are doing is showing that you don't understand proof by
contradiction,

Not at all. The COMPUTER SCIENCE of your requirements IS WRONG!

No, YOU don't understand what Computer Science actually is talking
about.

Every function computed by a model of computation must apply a specific
sequence of steps that are specified by the model to the actual finite
string input.

>

You are very confused. An algorithm or program computes a function.
>

>
Nothing computes a function unless it applies a specific
set of rules to its actual input to derive its output.
Anything that ignores its input is not computing a function.
>

>
Right, so HHH needs to apply the rules that it was designed with.
>
And that means it breaks the criteria that you say it needs to do to get the right answer,
>
And thus it gets the wrong answer.
>

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It needs to emulate DD according to the rules of
the x86 language. This includes emulating itself
emulating DD until it recognizes that if it kept
doing this that DD would never halt.

>
No, to be a correct emulator it needs to continue until it reaches the end,
>
It can get the right answer if it emulates the input to the point that it can show that a
>
>

>
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its
     input D until H correctly determines that its simulated D
     *would never stop running unless aborted* then

>
Right, that UTM(D) would never halt.
>

>
*would never stop running unless aborted*
Is the hypothetical HHH/DD pair where HHH does not abort.

>
>
Nope, can't change DD, it is your hypothetical HHH, which has become UTM, when given the ORIGINAL DD, which calls the ORIGINAL HHH, as that code was part of the definition of DD.

>
HHH bases its decision on what the behavior of DD
would be if a hypothetical version of its own self
never aborted.
>

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In other words, it bases it decision on a LIE.
>

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It bases its decision on exactly what Professor Sipser agreed to.

>
Nope
>

<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its
     input D until H correctly determines that its simulated D
     *would never stop running unless aborted* then
>
     H can abort its simulation of D and correctly report that D
     *specifies a non-halting sequence of configurations*.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>
     *simulated D would never stop running unless aborted* then
     *H can abort its simulation of D*
     *D specifies a non-halting sequence of configurations*
>
One hypothetical HHH that never aborts and
another different HHH that does abort.
>

>
But your Hypothetical HHH wasn't given the right input, because you never had one since you have admitted that D isn't a program as required and assumed by Professor Sipser.
>

Termination analyzers can be and have been applied to C functions.

But only C functions that represent PROGRAMS, i.e. that include all the code they will use.

 

To be correct, Hypothetical HHH is given real DD which uses the code of real HHH and then, when it does its simulation it will see that code of the real HHH abort its simulation

 As soon as HHH correctly determines
*simulated D would never stop running unless aborted* then
   It can see the same repeated state that we can all see.

But the simulation of DD does stop running even if that simulation is not aborted, as the HHH that DD calls *DOES* abort its simulaton, and thus a CORRECT simulation of that input will halt

    *H can abort its simulation of D*
   *D specifies a non-halting sequence of configurations*
 

But since the prerequisite doesn't happen (since you claim HHH does try to use the final clause) it lost its justifcation to do so.
Or, you are just admitting that you whole argument is a LIE as it was never about the required domain of Computations (aka Programs) because you were too ignorant of what that means.
It seems you have admitted to that level of stupidity, which seems to be a gross and reckless disregard for the truth, especially considering how many times you have been told it.