Re: Every sufficiently competent C programmer knows --- Semantic Property of Finite String

On 3/13/2025 12:05 AM, olcott wrote:

On 3/12/2025 9:49 PM, dbush wrote:

On 3/12/2025 10:41 PM, olcott wrote:

On 3/12/2025 7:56 PM, dbush wrote:

On 3/12/2025 8:41 PM, olcott wrote:>>

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NOT WHEN IT IS STIPULATED THAT THE BEHAVIOR BEING
MEASURED IS

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The direct execution of DDD

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is proven to be different than the behavior of DDD
emulated by HHH according to the semantics of the
x86 language.
>

>
Which is not what a solution to the halting problem is stipulated to compute:
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>

 Unless you look more deeply into these things and
realize that it is the semantic property of the
(computation encoded as a) finite string that Rice's
Theorem is based on.

And that semantic property is the direct execution of the program described by the input.

 

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

 The finite string pair DDD/HHH specifies a different
computation than the finite string pair DDD/HHH1.
 

False.  DDD is the description of the algorithm <DDD> which includes the fixed code of the function DDD, the fixed code of the function HHH (i.e. HHH is part of the input), and the fixed code of everything it calls down to the OS level.
So HHH(DDD) and HHH1(DDD) are both being passed the same program description and are therefore required to both compute the same mapping:
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