Re: Correcting the definition of the halting problem --- Computable functions

On 3/25/2025 3:54 AM, Mikko wrote:

On 2025-03-24 16:44:52 +0000, olcott said:
 

On 3/24/2025 10:14 AM, dbush wrote:

On 3/24/2025 11:03 AM, olcott wrote:

On 3/24/2025 6:23 AM, Richard Damon wrote:

On 3/23/25 11:09 PM, olcott wrote:

It is impossible for HHH compute the function from the direct
execution of DDD because DDD is not the finite string input
basis from which all computations must begin.
https://en.wikipedia.org/wiki/Computable_function

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WHy isn't DDD made into the correct finite string?i
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DDD is a semantically and syntactically correct finite
stirng of the x86 machine language.

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Which includes the machine code of DDD, the machine code of HHH, and the machine code of everything it calls down to the OS level.
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That seems to be your own fault.
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The problem has always been that you want to use the wrong string for DDD by excluding the code for HHH from it.
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DDD emulated by HHH directly causes recursive emulation
because it calls HHH(DDD) to emulate itself again. HHH
complies until HHH determines that this cycle cannot
possibly reach the final halt state of DDD.
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Which is another way of saying that HHH can't determine that DDD halts when executed directly.
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given an input of the function domain it can
return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
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Computable functions are only allowed to compute the
mapping from their input finite strings to an output.

 A comutable function does not compute. A Turing machine can compute
a value of a computable function.
 

Whenever I have referred to a computable function
I have always been referring to computable functions
implemented within some model of computation that
like Turing machines have finite strings as their
only input.

All computations are allowed. There are not other restrictions on
computable functions that that it must be a function and thane it
must be computable.
 

Computing who will win the next presidential election
on the basis of the finite string "the" violates what
computations are and how they work thus does not derive
any undecidable decision problem.
Likewise computing the behavior of the direct execution
of a Turing Machine based on its machine description can
be incorrect when this machine has defined a pathological
relationship with its emulator.
_III()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov  ebp,esp  ; housekeeping
[00002175] 6872210000 push 00002172 ; push III
[0000217a] e853f4ffff call 000015d2 ; call EEE(III)
[0000217f] 83c404     add  esp,+04
[00002182] 5d         pop  ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]
When any finite number of steps of III is emulated by
EEE according to the semantics of the x86 language the
emulated III never reaches its "ret" instruction final
halt state and the directly executed III does halt.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer