Re: How the requirements that Professor Sipser agreed to are exactly met

On 5/12/2025 10:46 PM, olcott wrote:

On 5/12/2025 8:00 PM, dbush wrote:

On 5/12/2025 8:56 PM, olcott wrote:

On 5/12/2025 7:36 PM, dbush wrote:

On 5/12/2025 8:34 PM, olcott wrote:

On 5/12/2025 7:27 PM, dbush wrote:

On 5/12/2025 8:25 PM, olcott wrote:

On 5/12/2025 7:12 PM, dbush wrote:

On 5/12/2025 7:53 PM, olcott wrote:

>
Simulating Termination analyzers cannot possibly report
on the actual behavior of non-terminating inputs
because this would cause themselves to never terminate.
>
They must always hypothesize what the behavior of the
input would be if they themselves never aborted.
>

>
False.  They must always hypothesize what the behavior of algorithm described by the input would be if it was executed directly, as per the requirements:
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Show the actual reasoning of how it makes sense
that a simulating termination analyzer should
ignore the behavior (to its own peril) that the
input actually specifies.

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There is no requirement that building a termination analyzer, simulating or otherwise, is possible.  In fact, it has proved to not be possible by Linz and others, which you have *explicitly* agreed with.
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In other words you have no such actual reasoning.

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The reasoning is that there is no requirement that building a termination analyzer is possible.

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So you have no actual reasoning that addresses my
actual point.
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 >>>> Show the actual reasoning of how it makes sense
 >>>> that a simulating termination analyzer should
 >>>> ignore the behavior (to its own peril) that the
 >>>> input actually specifies.
>

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It makes sense because that's what's required to tell me if any arbitrary algorithm X with input Y will halt when executed directly.
>

 A simulating termination analyzer(STA) reports on
the behavior of the direct execution of the
algorithm specified by its input except in the
case where the input calls this STA to try to fool it.
 What you are proposing would cause HHH to get stuck
in infinite execution. How is getting stuck in
infinite execution better than not getting stuck?

In other words, if you assume that a termination analyzer exists, i.e. something that meets the below requirements, you reach a contradiction. Therefore the assumption that the below requirements can be met is proven false, as Linz and others have proved and as you have *explicitly* agreed with.
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly

 

It would be *very* useful to me if I had an algorithm H that could tell me that in *all* possible cases.  If so, I could solve the Goldbach conjecture and make unknownable truths knowable, among many other unsolved problems.
 Does an algorithm H exist that can tell me that or not?