Re: Turing Machine computable functions apply finite string transformations to inputs +++

On 4/28/2025 5:47 PM, olcott wrote:

On 4/28/2025 3:21 PM, Richard Heathfield wrote:

On 28/04/2025 21:03, olcott wrote:

On 4/28/2025 2:58 PM, dbush wrote:

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Category error.  The halting function below is fully defined, and this mapping is not computable *as you have explicitly admitted*.
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Neither is the square root of an actual onion computable.
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Turing Computable Functions are required to apply finite
string transformations to their inputs. The function defined
below ignores that requirement PROVING THAT IT IS INCORRECT.

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No, it proves that you agree that it's not a computable function. QED.
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 Computing the actual behavior the direct execution
of any input is ALWAYS IMPOSSIBLE.

So you again agree that Linz is correct.

 No halt decider

So you assume that an algorithm exists that can perform the following mapping:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
(<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

can ever directly see the actual
behavior of any directly executed input.
 

And you reach a contradiction, proving the assumption false, as Linz proved and you *explicitly* agreed is correct.

Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
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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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