• Simplied Halting Problem and proof

    From wij@wyniijj5@gmail.com to comp.theory on Mon Sep 15 02:29:40 2025
    From Newsgroup: comp.theory

    As olcott had found recently, the 1,0 decision codes in HP is actually unreachable dead codes. The HP proof can be simplified as:
    extern int HHH(void (*)()); // the claimed halt decider. Also a suggest, making
     // HHH external can improve the quality of POOH
    void DD() {
    HHH(DD);
    }
    int main() {
    HHH(DD); // Does HHH halt?
    }
    HHH (in main) is obviously an infinite recurrsive call. It cannot return.
    Thus, Halt Problem is undecidable.
    'undecidable' really means an endless loop, not the toggle of 1's and 0's.
    E.g. The decision of truth value of "this sentence is true" is also undecidable,
    though not looking paradoxical. It is because the 'not looking paradoxical', many proofs or even theorem are actually based on self-referencial reasoning, e.g. Dedekind's real number theory, Cantor's set theory (and many POOH arguments
    are also self-referencial).
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  • From Mikko@mikko.levanto@iki.fi to comp.theory on Mon Sep 15 11:24:28 2025
    From Newsgroup: comp.theory

    On 2025-09-14 18:29:40 +0000, wij said:

    As olcott had found recently, the 1,0 decision codes in HP is actually unreachable dead codes.

    No, it is not. HP is about halting and nothing else. But both the halting problem and the dead code problem are special cases of reachability
    problems. If a full reachability analysis can be performed then that
    answers both the halting and dead code questions.
    --
    Mikko

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  • From wij@wyniijj5@gmail.com to comp.theory on Mon Sep 15 19:38:29 2025
    From Newsgroup: comp.theory

    On Mon, 2025-09-15 at 11:24 +0300, Mikko wrote:
    On 2025-09-14 18:29:40 +0000, wij said:

    As olcott had found recently, the 1,0 decision codes in HP is actually unreachable dead codes.

    No, it is not. HP is about halting and nothing else. But both the halting problem and the dead code problem are special cases of reachability
    problems. If a full reachability analysis can be performed then that
    answers both the halting and dead code questions.
    Correct. It is not dead code. The simplified proof is wrong. Thanks. Undecidable and self-reference are not exactly the same.
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  • From olcott@polcott333@gmail.com to comp.theory on Mon Sep 15 11:34:26 2025
    From Newsgroup: comp.theory

    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is actually unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)()); // the claimed halt decider. Also a suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot return. Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
    HHH(DDD);
    return;
    }

    Simulating Termination analyzer HHH(DDD)
    returns 0 because

    *HHH sees this on the basis that*
    (a) DDD calls the same function twice in sequence
    (b) With the same argument
    (c) DDD has no conditional branch instructions
    between the invocation of DDD and its call to HHH(DDD).

    'undecidable' really means an endless loop, not the toggle of 1's and 0's. E.g. The decision of truth value of "this sentence is true" is also undecidable,
    though not looking paradoxical. It is because the 'not looking paradoxical', many proofs or even theorem are actually based on self-referencial reasoning, e.g. Dedekind's real number theory, Cantor's set theory (and many POOH arguments
    are also self-referencial).

    --
    Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer
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  • From olcott@polcott333@gmail.com to comp.theory on Mon Sep 15 11:49:03 2025
    From Newsgroup: comp.theory

    On 9/15/2025 6:38 AM, wij wrote:
    On Mon, 2025-09-15 at 11:24 +0300, Mikko wrote:
    On 2025-09-14 18:29:40 +0000, wij said:

    As olcott had found recently, the 1,0 decision codes in HP is actually
    unreachable dead codes.

    No, it is not. HP is about halting and nothing else. But both the halting
    problem and the dead code problem are special cases of reachability
    problems. If a full reachability analysis can be performed then that
    answers both the halting and dead code questions.

    Correct. It is not dead code. The simplified proof is wrong. Thanks.

    Undecidable and self-reference are not exactly the same.


    People have been essentially brainwashed to believe
    that a halt decider is supposed to report on something
    besides the actual behavior that they actual input
    actually specifies. In this case *it is* dead code.
    --
    Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer
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  • From Kaz Kylheku@643-408-1753@kylheku.com to comp.theory on Mon Sep 15 17:33:15 2025
    From Newsgroup: comp.theory

    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    People have been essentially brainwashed to believe
    that a halt decider is supposed to report on something
    besides the actual behavior that they actual input

    In your apparatus, the simulated halt decider is peeking
    at a prior execution trace, not related to its input.

    Just by copy and pasting the decider function and changing
    its name, you obtain different results.

    Your shit is positively /not/ sticking to the doctrine of
    "actual behavior of actual input".
    --
    TXR Programming Language: http://nongnu.org/txr
    Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
    Mastodon: @Kazinator@mstdn.ca
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  • From Kaz Kylheku@643-408-1753@kylheku.com to comp.theory on Mon Sep 15 17:36:18 2025
    From Newsgroup: comp.theory

    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is actually
    unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)()); // the claimed halt decider. Also a suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot return.
    Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
    HHH(DDD);
    return;
    }

    Note that this is not exactly the diagonal "do the opposite" test case!

    Here, HHH(DDD) has the opportunity of correctly returning 1.


    Simulating Termination analyzer HHH(DDD)
    returns 0 because

    If HHH(DDD) returns 0, it means HHH(DDD) returns.

    If HHH(DD) returns, it means the above DDD reaches its return
    statement; i.e. terminates.

    So 0 is incorrect.

    Your shit cannot correctly decide even a trivial non-diagonal test
    case, if it only carries the vague scent of being a diagnoal
    test case by virtue of making a call to HHH(DDD).
    --
    TXR Programming Language: http://nongnu.org/txr
    Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
    Mastodon: @Kazinator@mstdn.ca
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  • From olcott@polcott333@gmail.com to comp.theory on Mon Sep 15 13:25:49 2025
    From Newsgroup: comp.theory

    On 9/15/2025 12:33 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    People have been essentially brainwashed to believe
    that a halt decider is supposed to report on something
    besides the actual behavior that they actual input

    In your apparatus, the simulated halt decider is peeking
    at a prior execution trace, not related to its input.


    void Infinite_Recursion()
    {
    Infinite_Recursion();
    return;
    }

    Because you are absolutely not going to believe me
    and you are a very smart guy I challenge you to
    derive all of the execution trace details of the
    criteria that HHH must use to conclusively prove that
    Infinite_Recursion() never halts.

    Just by copy and pasting the decider function and changing
    its name, you obtain different results.

    Your shit is positively /not/ sticking to the doctrine of
    "actual behavior of actual input".

    --
    Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer
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  • From olcott@polcott333@gmail.com to comp.theory on Mon Sep 15 13:27:00 2025
    From Newsgroup: comp.theory

    On 9/15/2025 12:36 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is actually
    unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)()); // the claimed halt decider. Also a suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot return. >>> Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
    HHH(DDD);
    return;
    }

    Note that this is not exactly the diagonal "do the opposite" test case!



    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES


    Here, HHH(DDD) has the opportunity of correctly returning 1.


    Simulating Termination analyzer HHH(DDD)
    returns 0 because

    If HHH(DDD) returns 0, it means HHH(DDD) returns.

    If HHH(DD) returns, it means the above DDD reaches its return
    statement; i.e. terminates.

    So 0 is incorrect.

    Your shit cannot correctly decide even a trivial non-diagonal test
    case, if it only carries the vague scent of being a diagnoal
    test case by virtue of making a call to HHH(DDD).

    --
    Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer
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  • From Mr Flibble@flibble@red-dwarf.jmc.corp to comp.theory on Mon Sep 15 18:51:58 2025
    From Newsgroup: comp.theory

    On Mon, 15 Sep 2025 13:25:49 -0500, olcott wrote:

    On 9/15/2025 12:33 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    People have been essentially brainwashed to believe that a halt
    decider is supposed to report on something besides the actual behavior
    that they actual input

    In your apparatus, the simulated halt decider is peeking at a prior
    execution trace, not related to its input.


    void Infinite_Recursion()
    {
    Infinite_Recursion();
    return;
    }

    Because you are absolutely not going to believe me and you are a very
    smart guy I challenge you to derive all of the execution trace details
    of the criteria that HHH must use to conclusively prove that Infinite_Recursion() never halts.

    Just by copy and pasting the decider function and changing its name,
    you obtain different results.

    Your shit is positively /not/ sticking to the doctrine of "actual
    behavior of actual input".


    Input halts.

    /Flibble
    --
    meet ever shorter deadlines, known as "beat the clock"
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  • From Mr Flibble@flibble@red-dwarf.jmc.corp to comp.theory on Mon Sep 15 18:52:50 2025
    From Newsgroup: comp.theory

    On Mon, 15 Sep 2025 13:27:00 -0500, olcott wrote:

    On 9/15/2025 12:36 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is
    actually unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)()); // the claimed halt decider. Also a
    suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot
    return.
    Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
    HHH(DDD);
    return;
    }

    Note that this is not exactly the diagonal "do the opposite" test case!



    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR
    THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE
    ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL
    INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT
    ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES
    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR
    THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE
    ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL
    INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT
    ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES


    Here, HHH(DDD) has the opportunity of correctly returning 1.


    Simulating Termination analyzer HHH(DDD)
    returns 0 because

    If HHH(DDD) returns 0, it means HHH(DDD) returns.

    If HHH(DD) returns, it means the above DDD reaches its return
    statement; i.e. terminates.

    So 0 is incorrect.

    Your shit cannot correctly decide even a trivial non-diagonal test
    case, if it only carries the vague scent of being a diagnoal test case
    by virtue of making a call to HHH(DDD).



    DD halts.

    /Flibble
    --
    meet ever shorter deadlines, known as "beat the clock"
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  • From Kaz Kylheku@643-408-1753@kylheku.com to comp.theory on Mon Sep 15 19:33:09 2025
    From Newsgroup: comp.theory

    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/15/2025 12:36 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is actually >>>> unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)()); // the claimed halt decider. Also a suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot return. >>>> Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
    HHH(DDD);
    return;
    }

    Note that this is not exactly the diagonal "do the opposite" test case!


    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES

    The actual behavior that the above actual input specifies is
    terminating, if HHH(DDD) returns any value whatsoever.

    The correct return vaue from HHH(DDD) is 1, which is achievable.

    We can substitute a definition of HHH which returns 1.

    I think that if HHH starts a simulation of DDD and steps it to
    completion, and then returns 1, it will work. No abort testing needed.

    Just allocate Registers, do the Debug_Step and return 1 when that
    indicates a return.

    Is it not working for you?
    --
    TXR Programming Language: http://nongnu.org/txr
    Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
    Mastodon: @Kazinator@mstdn.ca
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory on Mon Sep 15 14:37:57 2025
    From Newsgroup: comp.theory

    On 9/15/2025 2:33 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/15/2025 12:36 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is actually >>>>> unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)()); // the claimed halt decider. Also a suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot return. >>>>> Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
    HHH(DDD);
    return;
    }

    Note that this is not exactly the diagonal "do the opposite" test case!


    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES

    The actual behavior that the above actual input specifies is
    terminating,

    void Infinite_Recursion()
    {
    Infinite_Recursion();
    return;
    }

    Then I must insist that you figure out the execution
    trace criteria that HHH would use to prove that its
    of simulation of Infinite_Recursion is definitely not
    halting before we proceed.

    I already gave it you you and you rejected it
    out-of-hand. Now its your turn to do the actual thinking.
    --
    Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer
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  • From Ben Bacarisse@ben@bsb.me.uk to comp.theory on Mon Sep 15 23:20:31 2025
    From Newsgroup: comp.theory

    wij <wyniijj5@gmail.com> writes:

    ... The HP proof can be simplified as:

    (I'll ignore all the problems with what looks like C code. Let's just
    think of it as pseudo code.)

    extern int HHH(void (*)()); // the claimed halt decider. Also a
    suggest, making
     // HHH external can improve the quality of POOH

    void DD() {
    HHH(DD);
    }

    int main() {
    HHH(DD); // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot
    return.

    Nonsense. Some specific implementations of HHH might cause the call in
    main to not return, but you don't show the body HHH.

    What we know (from the real mathematics) is that no implementation of
    HHH can determine if the function passed to it always returns. Indeed
    we know no implementation of HHH can determine any non-trivial property
    of the functions it can be passed.

    Thus, Halt Problem is undecidable.

    Your outline shows nothing about halting,
    --
    Ben.
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  • From Fred. Zwarts@F.Zwarts@HetNet.nl to comp.theory on Tue Sep 16 10:04:18 2025
    From Newsgroup: comp.theory

    Op 15.sep.2025 om 21:37 schreef olcott:
    On 9/15/2025 2:33 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/15/2025 12:36 PM, Kaz Kylheku wrote:
    On 2025-09-15, olcott <polcott333@gmail.com> wrote:
    On 9/14/2025 1:29 PM, wij wrote:
    As olcott had found recently, the 1,0 decision codes in HP is
    actually
    unreachable dead codes. The HP proof can be simplified as:

    extern int HHH(void (*)());  // the claimed halt decider. Also a >>>>>> suggest, making
        // HHH external can improve the quality of POOH

    void DD() {
        HHH(DD);
    }

    int main() {
        HHH(DD);        // Does HHH halt?
    }

    HHH (in main) is obviously an infinite recurrsive call. It cannot >>>>>> return.
    Thus, Halt Problem is undecidable.


    *I do this same thing with*
    void DDD()
    {
         HHH(DDD);
         return;
    }

    Note that this is not exactly the diagonal "do the opposite" test case! >>>

    THE ACTUAL BEHAVIOR THAT THE ACTUAL INPUT ACTUALLY SPECIFIES

    The actual behavior that the above actual input specifies is
    terminating,

    void Infinite_Recursion()
    {
      Infinite_Recursion();
      return;
    }

    Then I must insist that you figure out the execution
    trace criteria that HHH would use to prove that its
    of simulation of Infinite_Recursion is definitely not
    halting before we proceed.

    It is impossible to make a decider that is correct for all possible inputs. That said, HHH can see that there are no conditional branch instructions
    in between two successive calls to Infinite_Recursion.
    That is what makes Infinite_Recursion different from DDD, where there
    are many conditional branch instruction between two successive starting
    points of a new simulation.
    HHH fails to analyse the changing conditions for these conditional
    branch instructions. If it did, it would see that after two cycles the conditions are met for another branch.
    HHH does not do that, so after seeing a few recursions, it can only
    assume that the recursion is infinite, whereas even a beginner in
    programming sees that the recursion is finite.

    You have programmed your belief that what you do not see does not exists
    in HHH. It is made blind for the finite recursion, so it incorrectly
    pretends that there is an infinite recursion.

    You know this and you don't know a counter argument, so here comes your attitude again: close your eyes for it and pretend that it does not exist.
    We will see again that you will not find a counter argument and you will ignore that your claims are debunked.
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  • From Mikko@mikko.levanto@iki.fi to comp.theory on Tue Sep 16 11:43:41 2025
    From Newsgroup: comp.theory

    On 2025-09-15 11:38:29 +0000, wij said:

    On Mon, 2025-09-15 at 11:24 +0300, Mikko wrote:
    On 2025-09-14 18:29:40 +0000, wij said:

    As olcott had found recently, the 1,0 decision codes in HP is actually
    unreachable dead codes.

    No, it is not. HP is about halting and nothing else. But both the halting
    problem and the dead code problem are special cases of reachability
    problems. If a full reachability analysis can be performed then that
    answers both the halting and dead code questions.

    Correct. It is not dead code. The simplified proof is wrong. Thanks.

    Undecidable and self-reference are not exactly the same.

    There is no self-reference in a Turing machine. Whether a Turing machine
    with a specific input halts is not undecidable for any pair of a Turing
    macine and input.
    --
    Mikko

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