Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 5:47 PM, olcott wrote:

On 5/5/2025 4:40 PM, Richard Heathfield wrote:

On 05/05/2025 22:31, dbush wrote:

On 5/5/2025 5:08 PM, olcott wrote:

>
<snip>
>

No TM can compute the square root of a dead rabbit either.

>
Strawman.  The square root of a dead rabbit does not exist,

>
Don't be so sure. I have several on my mantelpiece and two more on order. For once, olcott is right; there is no way to compute them. They do, however, need thorough and regular polishing. Black polish or brown? Well, that's undecidable.
>

but the question of whether any arbitrary algorithm X with input Y halts when executed directly has a correct answer in all cases.

>
Indeed it has.
>

It's just that no algorithm exists that can compute that mapping, as proven by Linz and other and as you have *explicitly* agreed is correct.

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He's coming round to the idea, albeit slowly. He can't bring himself to describe the mapping as 'incomputable' or 'undecidable', but he's started to claim that such a mapping is 'incorrect', which is a tacit acknowledgement that it exists.
>

 When the input to HHH(DD) is mapped to the
behavior that this input actually specifies
IT DOES NOT HALT.
 

In other words, HHH doesn't meet the requirements to be a solution to the halting problem:
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

That everyone stupidly imagines that DD emulated
by HHH according to the rules of the x86 language

Which is does not correctly do, as you have admitted on the record:
On 5/5/2025 8:24 AM, dbush wrote:
 > On 5/4/2025 11:03 PM, dbush wrote:
 >> On 5/4/2025 10:05 PM, olcott wrote:
 >>> On 5/4/2025 7:23 PM, Richard Damon wrote:
 >>>> But HHH doesn't correct emulated DD by those rules, as those rules
 >>>> do not allow HHH to stop its emulation,
 >>>
 >>> Sure they do you freaking moron...
 >>
 >> Then show where in the Intel instruction manual that the execution of
 >> any instruction other than a HLT is allowed to stop instead of
 >> executing the next instruction.
 >>
 >> Failure to do so in your next reply, or within one hour of your next
 >> post on this newsgroup, will be taken as you official on-the-record
 >> admission that there is no such allowance and that HHH does NOT
 >> correctly simulate DD.
 >
 > Let the record show that Peter Olcott made the following post in this
 > newsgroup after the above message:
 >
 > On 5/4/2025 11:04 PM, olcott wrote:
 >  > D *WOULD NEVER STOP RUNNING UNLESS*
 >  > indicates that professor Sipser was agreeing
 >  > to hypotheticals AS *NOT CHANGING THE INPUT*
 >  >
 >  > You are taking
 >  > *WOULD NEVER STOP RUNNING UNLESS*
 >  > to mean *NEVER STOPS RUNNING* that is incorrect.
 >
 > And has made no attempt after over 9 hours to show where in the Intel
 > instruction manual that execution is allowed to stop after any
 > instruction other than HLT.
 >
 > Therefore, as per the above criteria:
 >
 > LET THE RECORD SHOW
 >
 > That Peter Olcott
 >
 > Has *officially* admitted
 >
 > That DD is NOT correctly simulated by HHH