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

Liste des GroupesRevenir à theory 
Sujet : Re: Turing Machine computable functions apply finite string transformations to inputs +++
De : rjh (at) *nospam* cpax.org.uk (Richard Heathfield)
Groupes : comp.theory
Date : 28. Apr 2025, 21:21:32
Autres entêtes
Organisation : Fix this later
Message-ID : <vuoo0c$2g74$3@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
User-Agent : Mozilla Thunderbird
On 28/04/2025 21:03, olcott wrote:
On 4/28/2025 2:58 PM, dbush wrote:
<snip>

Category error.  The halting function below is fully defined, and this mapping is not computable *as you have explicitly admitted*.
>
 Neither is the square root of an actual onion computable.
 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.
No, it proves that you agree that it's not a computable function. QED.

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
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

Date Sujet#  Auteur
21 Apr 25 * Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error450Keith Thompson
22 Apr 25 +* Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error442olcott
22 Apr 25 i+- Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error1Richard Damon
25 Apr 25 i`* Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error440olcott
25 Apr 25 i +* Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error195Richard Damon
25 Apr 25 i i`* Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error194olcott
25 Apr 25 i i +* Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error192joes
26 Apr 25 i i i`* Turing Machine computable functions apply finite string transformations to inputs191olcott
26 Apr 25 i i i +- Re: Turing Machine computable functions apply finite string transformations to inputs1dbush
26 Apr 25 i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs188joes
26 Apr 25 i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs187olcott
26 Apr 25 i i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs185Fred. Zwarts
26 Apr 25 i i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs184olcott
26 Apr 25 i i i i i +- Re: Turing Machine computable functions apply finite string transformations to inputs1dbush
26 Apr 25 i i i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs181Richard Damon
26 Apr 25 i i i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs180olcott
26 Apr 25 i i i i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs172dbush
26 Apr 25 i i i i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs171olcott
26 Apr 25 i i i i i i i `* Re: Turing Machine computable functions apply finite string transformations to inputs170dbush
27 Apr 25 i i i i i i i  `* Re: Turing Machine computable functions apply finite string transformations to inputs169olcott
27 Apr 25 i i i i i i i   +* Re: Turing Machine computable functions apply finite string transformations to inputs137dbush
27 Apr 25 i i i i i i i   i`* Re: Turing Machine computable functions apply finite string transformations to inputs136olcott
27 Apr 25 i i i i i i i   i +* Re: Turing Machine computable functions apply finite string transformations to inputs134dbush
27 Apr 25 i i i i i i i   i i+* Re: Turing Machine computable functions apply finite string transformations to inputs132olcott
27 Apr 25 i i i i i i i   i ii+* Re: Turing Machine computable functions apply finite string transformations to inputs5dbush
28 Apr 25 i i i i i i i   i iii`* Re: Turing Machine computable functions apply finite string transformations to inputs4olcott
28 Apr 25 i i i i i i i   i iii +- Re: Turing Machine computable functions apply finite string transformations to inputs1joes
28 Apr 25 i i i i i i i   i iii +- Re: Turing Machine computable functions apply finite string transformations to inputs1Richard Damon
28 Apr 25 i i i i i i i   i iii `- Re: Turing Machine computable functions apply finite string transformations to inputs1dbush
28 Apr 25 i i i i i i i   i ii+- Re: Turing Machine computable functions apply finite string transformations to inputs1Richard Damon
28 Apr 25 i i i i i i i   i ii`* Re: Turing Machine computable functions apply finite string transformations to inputs125Fred. Zwarts
28 Apr 25 i i i i i i i   i ii `* Re: Turing Machine computable functions apply finite string transformations to inputs124Richard Heathfield
28 Apr 25 i i i i i i i   i ii  `* Re: Turing Machine computable functions apply finite string transformations to inputs123olcott
28 Apr 25 i i i i i i i   i ii   +* Re: Turing Machine computable functions apply finite string transformations to inputs15dbush
28 Apr 25 i i i i i i i   i ii   i`* Re: Turing Machine computable functions apply finite string transformations to inputs14olcott
28 Apr 25 i i i i i i i   i ii   i +* Re: Turing Machine computable functions apply finite string transformations to inputs11dbush
28 Apr 25 i i i i i i i   i ii   i i`* Re: Turing Machine computable functions apply finite string transformations to inputs10olcott
28 Apr 25 i i i i i i i   i ii   i i +* Re: Turing Machine computable functions apply finite string transformations to inputs7dbush
28 Apr 25 i i i i i i i   i ii   i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs6olcott
28 Apr 25 i i i i i i i   i ii   i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs4dbush
28 Apr 25 i i i i i i i   i ii   i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs3olcott
28 Apr 25 i i i i i i i   i ii   i i i i +- Re: Turing Machine computable functions apply finite string transformations to inputs1dbush
29 Apr 25 i i i i i i i   i ii   i i i i `- Re: Turing Machine computable functions apply finite string transformations to inputs1Richard Damon
29 Apr 25 i i i i i i i   i ii   i i i `- Re: Turing Machine computable functions apply finite string transformations to inputs1Richard Damon
28 Apr 25 i i i i i i i   i ii   i i +- Re: Turing Machine computable functions apply finite string transformations to inputs1Fred. Zwarts
29 Apr 25 i i i i i i i   i ii   i i `- Re: Turing Machine computable functions apply finite string transformations to inputs1Richard Damon
29 Apr 25 i i i i i i i   i ii   i `* Re: Turing Machine computable functions apply finite string transformations to inputs2Richard Damon
29 Apr 25 i i i i i i i   i ii   i  `- Re: Turing Machine computable functions apply finite string transformations to inputs1Richard Heathfield
28 Apr 25 i i i i i i i   i ii   +- Re: Turing Machine computable functions apply finite string transformations to inputs1joes
28 Apr 25 i i i i i i i   i ii   +* Re: Turing Machine computable functions apply finite string transformations to inputs104Richard Heathfield
28 Apr 25 i i i i i i i   i ii   i`* Re: Turing Machine computable functions apply finite string transformations to inputs103olcott
28 Apr 25 i i i i i i i   i ii   i +* Re: Turing Machine computable functions apply finite string transformations to inputs14dbush
28 Apr 25 i i i i i i i   i ii   i i`* Re: Turing Machine computable functions apply finite string transformations to inputs +++13olcott
28 Apr 25 i i i i i i i   i ii   i i `* Re: Turing Machine computable functions apply finite string transformations to inputs +++12dbush
28 Apr 25 i i i i i i i   i ii   i i  `* Re: Turing Machine computable functions apply finite string transformations to inputs +++11olcott
28 Apr 25 i i i i i i i   i ii   i i   `* Re: Turing Machine computable functions apply finite string transformations to inputs +++10dbush
28 Apr 25 i i i i i i i   i ii   i i    `* Re: Turing Machine computable functions apply finite string transformations to inputs +++9olcott
28 Apr 25 i i i i i i i   i ii   i i     +* Re: Turing Machine computable functions apply finite string transformations to inputs +++2dbush
28 Apr 25 i i i i i i i   i ii   i i     i`- Re: Turing Machine computable functions apply finite string transformations to inputs +++1Richard Heathfield
28 Apr 25 i i i i i i i   i ii   i i     +- Re: Turing Machine computable functions apply finite string transformations to inputs +++1Fred. Zwarts
28 Apr 25 i i i i i i i   i ii   i i     `* Re: Turing Machine computable functions apply finite string transformations to inputs +++5Richard Heathfield
28 Apr 25 i i i i i i i   i ii   i i      `* Re: Turing Machine computable functions apply finite string transformations to inputs +++4olcott
28 Apr 25 i i i i i i i   i ii   i i       +- Re: Turing Machine computable functions apply finite string transformations to inputs +++1dbush
28 Apr 25 i i i i i i i   i ii   i i       +- Re: Turing Machine computable functions apply finite string transformations to inputs +++1Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i i       `- Re: Turing Machine computable functions apply finite string transformations to inputs +++1joes
28 Apr 25 i i i i i i i   i ii   i +* Re: Turing Machine computable functions DON'T apply finite string transformations to inputs2Alan Mackenzie
28 Apr 25 i i i i i i i   i ii   i i`- Re: Turing Machine computable functions DON'T apply finite string transformations to inputs1olcott
28 Apr 25 i i i i i i i   i ii   i `* Re: Turing Machine computable functions apply finite string transformations to inputs86Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i  `* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT85olcott
29 Apr 25 i i i i i i i   i ii   i   +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT7dbush
29 Apr 25 i i i i i i i   i ii   i   i`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT6olcott
29 Apr 25 i i i i i i i   i ii   i   i +- Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT1Fred. Zwarts
29 Apr 25 i i i i i i i   i ii   i   i +- Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT1Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i   i +- Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT1Richard Damon
29 Apr 25 i i i i i i i   i ii   i   i `* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT2dbush
29 Apr 25 i i i i i i i   i ii   i   i  `- Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT1dbush
29 Apr 25 i i i i i i i   i ii   i   +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT65Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i   i`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT64olcott
29 Apr 25 i i i i i i i   i ii   i   i +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT48Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i   i i`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT47olcott
29 Apr 25 i i i i i i i   i ii   i   i i +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT45Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i   i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT44olcott
29 Apr 25 i i i i i i i   i ii   i   i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT42Richard Heathfield
29 Apr 25 i i i i i i i   i ii   i   i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT41olcott
29 Apr 25 i i i i i i i   i ii   i   i i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT39Richard Heathfield
30 Apr 25 i i i i i i i   i ii   i   i i i i i`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT38olcott
30 Apr 25 i i i i i i i   i ii   i   i i i i i +* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT35Richard Heathfield
30 Apr 25 i i i i i i i   i ii   i   i i i i i i+* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT15olcott
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30 Apr 25 i i i i i i i   i ii   i   i i i i i ii+- Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT1dbush
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30 Apr 25 i i i i i i i   i ii   i   i i i i i iii`* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT10olcott
30 Apr 25 i i i i i i i   i ii   i   i i i i i iii `* Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT9Keith Thompson
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