Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets

Liste des GroupesRevenir à s logic 
Sujet : Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : comp.theory sci.logic
Date : 29. May 2024, 04:04:14
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <v362eu$2d367$3@i2pn2.org>
References : 1
User-Agent : Mozilla Thunderbird
On 5/28/24 12:16 PM, olcott wrote:
typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         int Halt_Status = H(p, p);
04         if (Halt_Status)
05           HERE: goto HERE;
06         return Halt_Status;
07       }
08
09       int main()
10       {
11         H(D,D);
12         return 0;
13       }
 When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
 *Formalizing the Linz Proof structure*
∃H  ∈ Turing_Machines
∀x  ∈ Turing_Machines_Descriptions
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,x)
But since for x being the description of the H^ built from that H and y being the same, it turns out that no matter what answer H gives, it will be wrong.
(And I think you have an error in your reference to Halts, I think you mean Halts(x,y) not Halts(x,x)

 *Here is the same thing applied to H/D pairs*
∃H ∈ C_Functions
∀D ∈ x86_Machine_Code_of_C_Functions
such that H(D,D) = Halts(D,D)
Not the same thing.
∃H ∈ C_Functions
is not equivalent to
∃H  ∈ Turing_Machines
as there are many C_Functions that are not the equivalent of Turing Machines.

 In both cases infinite sets are examined to see
if any H exists with the required properties.
 
Yes, but the logic of Turing Machines looks at them one at a time, and the input is a FULL INDEPENDENT PROGRAM.
I'm not sure what you can define your computation system to be actually based on, and what its supposed use is, since your 'decider' and 'input' are so intertwined.
And your supposed algorithm just doesn't work when you try to make you system "Turing Complete" by letting D have the ability to have a COPY of H, and being able to make copies of its input, like real Turing machines can.

Date Sujet#  Auteur
28 May 24 * D correctly simulated by H cannot possibly halt --- templates and infinite sets253olcott
29 May 24 +* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets214Richard Damon
29 May 24 i`* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets213olcott
29 May 24 i `* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets212Richard Damon
29 May 24 i  `* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets211olcott
29 May 24 i   +* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets194Richard Damon
29 May 24 i   i`* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets193olcott
29 May 24 i   i +* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets191Alan Mackenzie
29 May 24 i   i i+- Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets1olcott
29 May 24 i   i i`* Two dozen people were simply wrong189olcott
29 May 24 i   i i +* Re: Two dozen people were simply wrong3Alan Mackenzie
29 May 24 i   i i i+- Re: Two dozen people were simply wrong1olcott
29 May 24 i   i i i`- Re: Two dozen people were simply wrong1olcott
30 May 24 i   i i +* Re: Two dozen people were simply wrong (including Olcott)178Richard Damon
30 May 24 i   i i i`* Re: Two dozen people were simply wrong --- Try to prove otherwise177olcott
30 May 24 i   i i i `* Re: Two dozen people were simply wrong --- Try to prove otherwise176Richard Damon
30 May 24 i   i i i  `* Re: Two dozen people were simply wrong --- Try to prove otherwise175olcott
30 May 24 i   i i i   `* Re: Two dozen people were simply wrong --- Try to prove otherwise174Richard Damon
30 May 24 i   i i i    `* Re: Two dozen people were simply wrong --- Try to prove otherwise173olcott
30 May 24 i   i i i     `* Re: Two dozen people were simply wrong --- Try to prove otherwise172Richard Damon
30 May 24 i   i i i      `* Re: Two dozen people were simply wrong --- Try to prove otherwise171olcott
30 May 24 i   i i i       +* Re: Two dozen people were simply wrong --- Try to prove otherwise11Richard Damon
30 May 24 i   i i i       i+* Re: Two dozen people were simply wrong --- Try to prove otherwise2olcott
30 May 24 i   i i i       ii`- Re: Two dozen people were simply wrong --- Try to prove otherwise1Richard Damon
30 May 24 i   i i i       i`* Re: Two dozen people were simply wrong --- Try to prove otherwise8olcott
30 May 24 i   i i i       i `* Re: Two dozen people were simply wrong --- Try to prove otherwise7Richard Damon
30 May 24 i   i i i       i  `* Re: Two dozen people were simply wrong --- Try to prove otherwise6olcott
30 May 24 i   i i i       i   `* Re: Two dozen people were simply wrong --- Try to prove otherwise5Richard Damon
30 May 24 i   i i i       i    `* Re: Two dozen people were simply wrong --- Try to prove otherwise4olcott
30 May 24 i   i i i       i     `* Re: Olcott was simply wrong --- Try to prove otherwise3Richard Damon
30 May 24 i   i i i       i      `* Re: Olcott was simply wrong --- Try to prove otherwise2olcott
31 May 24 i   i i i       i       `- Re: Olcott was simply wrong --- Try to prove otherwise1Richard Damon
31 May 24 i   i i i       `* Re: Two dozen people were simply wrong --- Try to prove otherwise159olcott
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1 Jun 24 i   i i i        i          `* Re: Two dozen people were simply wrong --- Try to prove otherwise --- pinned down146olcott
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1 Jun 24 i   i i i        i           i`* Re: Two dozen people were simply wrong --- Try to prove otherwise --- pinned down143olcott
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30 May 24 `* Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets --- deciders38olcott

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