Re: Halting Problem: What Constitutes Pathological Input

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

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

On 5/5/2025 8:30 PM, olcott wrote:

On 5/5/2025 7:18 PM, dbush wrote:

On 5/5/2025 8:14 PM, olcott wrote:

On 5/5/2025 7:02 PM, dbush wrote:

On 5/5/2025 7:29 PM, olcott wrote:

On 5/5/2025 5:33 PM, dbush wrote:

On 5/5/2025 6:27 PM, olcott wrote:

On 5/5/2025 4:58 PM, dbush wrote:

On 5/5/2025 5:39 PM, olcott wrote:

On 5/5/2025 4:31 PM, dbush wrote:

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

On 5/5/2025 3:14 PM, dbush wrote:

On 5/5/2025 4:10 PM, olcott wrote:

On 5/5/2025 3:00 PM, dbush wrote:

On 5/5/2025 3:54 PM, olcott wrote:

On 5/5/2025 2:49 PM, dbush wrote:

On 5/5/2025 3:38 PM, olcott wrote:

On 5/5/2025 2:23 PM, Richard Heathfield wrote:

On 05/05/2025 20:20, olcott wrote:

Is "halts" the correct answer for H to return?  NO
Is "does not halt" the correct answer for H to return?  NO
Both Boolean return values are the wrong answer

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Or to put it another way, the answer is undecidable, QED.
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See? You got there in the end.
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Is this sentence true or false: "What time is it?"
is also "undecidable" because it is not a proposition
having a truth value.
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Is this sentence true or false: "This sentence is untrue."
is also "undecidable" because it is not a semantically sound
proposition having a truth value.
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Can Carol correctly answer “no” to this (yes/no) question?
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Both Yes and No are the wrong answer proving that
the question is incorrect when the context of who
is asked is understood to be a linguistically required
aspect of the full meaning of the question.

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And "does algorthm X with input Y halt when executed directly" has a single well defined answer.
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That is not even the actual question.
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In other words, you don't understand what the halting problem is about, because that is EXACTLY the question.
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That question is in many textbooks yet is still
wrong because functions computed by models of
computation such as Turing Machines or RASP machines
are only allowed to use actual inputs as their basis.

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And no Turing machine can compute the following mapping, as proven by Linz and other and as you have *explicitly* agreed is correct.
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No TM can compute the square root of a dead rabbit either.

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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.
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It has a correct answer that cannot ever be computed

Excellent!  So you once again *explicitly* agree that the theorem that the halting problem proofs prove is correct.
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because

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The existence of an algorithm that meets those requirements creates contradictions.

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It is the problem incorrect specification that creates
the contradiction.

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The fact that any arbitrary algorithm X with input Y either halts or does not halt when executed directly proves that false.
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Everyone here insists that functions computed
by models of computation can ignore inputs and
base their output on something else.
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THAT IS VERY STUPIDLY VERY WRONG.
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No, we just say that no algorithm can compute the above in all cases, as Linz and others have proves and as you have *explicitly* agreed is correct.

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FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
FROM INPUTS --- FROM INPUTS --- FROM INPUTS
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I'll let you respond to yourself:
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I keep telling you and conclusively proving
that both the Linz counter example input
and my fully specified termination analyzer

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Which starts with the assumption that an algorithm exists that performs the following mapping:
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Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
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A solution to the halting problem is an algorithm H that computes the following mapping:
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(<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
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DO COMPUTE THAT THE INPUT IS NON-HALTING
IFF (if and only if) the mapping FROM INPUTS
IS COMPUTED.

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

All you are doing is showing that you don't understand proof by contradiction, a concept taught to and understood by high school students more than 50 years your junior.
When the assumption is made that the above mapping is computable, we arrive at a contradiction.  That proves the assumption false.  It doesn't matter what the contradiction is.

 

Therefore the assumption that an algorithm exists that performs the above mapping is proven false, as Linz and others have show and as you have *explicitly* agreed is correct.
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