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

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:
>

 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.

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.
On 3/24/2025 10:07 PM, olcott wrote:
 > A halt decider cannot exist
On 4/28/2025 2:47 PM, olcott wrote:
 > On 4/28/2025 11:54 AM, dbush wrote:
 >> And the halting function below is not a computable function:
 >>
 >
 > It is NEVER a computable function
 >
 >> 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
On 3/14/2025 1:19 PM, olcott wrote:
 > When we define the HP as having H return a value
 > corresponding to the halting behavior of input D
 > and input D can actually does the opposite of whatever
 > value that H returns, then we have boxed ourselves
 > in to a problem having no solution.
On 6/21/2024 1:22 PM, olcott wrote:
 > the logical impossibility of specifying a halt decider H
 > that correctly reports the halt status of input D that is
 > defined to do the opposite of whatever value that H reports.
 > Of course this is impossible.
On 7/4/2023 12:57 AM, olcott wrote:
 > If you frame the problem in that a halt decider must divide up finite
 > strings pairs into those that halt when directly executed and those that
 > do not, then no single program can do this.
On 5/5/2025 5:39 PM, olcott wrote:
 > On 5/5/2025 4:31 PM, dbush wrote:
 >> Strawman.  The square root of a dead rabbit does not exist, but the
 >> question of whether any arbitrary algorithm X with input Y halts when
 >> executed directly has a correct answer in all cases.
 >>
 >
 > It has a correct answer that cannot ever be computed