Re: Proof that H(D,D) meets its abort criteria --induction criteria--

On 3/20/2024 2:11 PM, Fred. Zwarts wrote:

Op 20.mrt.2024 om 19:35 schreef olcott:

On 3/20/2024 1:13 PM, Richard Damon wrote:

On 3/20/24 12:29 PM, olcott wrote:

On 3/20/2024 11:12 AM, Richard Damon wrote:

On 3/19/24 2:14 PM, olcott wrote:

On 3/19/2024 12:42 PM, immibis wrote:

On 19/03/24 05:37, olcott wrote:

You are just getting nutty now. You are tossing out the sequence, selection, iteration model of computation.

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aren't you tossing out the turing machine model of computation?
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I am only tossing out the halting problem specification.
I am not saying (like Richard is saying) that sequential
code can be executed out-of-sequence.
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Just more of your lies.
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Where did I say "Sequential Code" can run out-of-sequence.
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THe codes that I talk about not being in the sequence you think are two INDEPENDENT copies of the machines.
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The one that is called first is executed first.

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And I never denied that.
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But H(D,D) doesn't "Call" D(D), it simulates it.
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Thus the steps of D(D) simulated by H come after H(D,D)
is executed, they do not occur in parallel at the same time.
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The D(D) that it simulates is a machine that has already been "run", since Turing Machines are FULL computation devices that run their procesisng as soon as they are created.
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In some strawman deception argument the steps of D(D) come
before H(D,D) is executed.
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This seems something you don't understand, because you seem to think that D(D) doesn't actually "run" until it is simulated.
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The steps of the simulated D(D) are never run, they are only simulated.
In a strawman deception argument the steps of D(D) are executed before
the steps of H(D,D).
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The H that is deciding the D(D) does not enforce that the ACTUAL D(D) it is simulating has not been run yet, and in fact, since we can consider Turing Machines to "auto-start" once created, it is IMPOSSIBLE to give to H a description of a D(D) that has not already run itself.
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The one that is called first is executed first.

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So?
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You tried to get away with saying otherwise.
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Where does H call D(D)? It SIMULATES it.
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You seem to think that simulation is the exact same thing as EXECUTION.
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Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
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Ĥ ⟨Ĥ⟩ is executed before Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ thus the executed Ĥ ⟨Ĥ⟩ is
run before the simulated one. When Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ simulates its input
it can see that it must abort this simulation.

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Yes H^ (H^) is executed before H^.H (H^) (H^) but the instance of the machine represented by that input was executed when it was created, so has already run.
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Unless you are trying to get away with rejecting the sequence of
sequence, selection, iteration you already know that Ĥ ⟨Ĥ⟩ is always
executed before Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩.
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Again, you are confusing the simulation that H, or H^.H does, with the axtual execution of them.
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You could even look at the simulation of H^.H as telling H part of what this H^ (H^) has alteady done.
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We, as finite humans may not know what it did, but the mathematical world of truth does.
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Mathematical induction proves that after N steps of correct simulation
H correctly determines that ∞ steps of correct simulation would never
halt. *These are verified facts that you perpetually deny*

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NOPE.
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STATE YOUR INDUCTION CRITERIA and their proof
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As soon as H(D,D) sees that D calls itself with its same inputs
and there are no conditional branch instructions from the
beginning of D to its call to H(D,D) then H knows that its
simulated D(D) cannot possibly reach its own final instruction
(at line 06) in any finite number of steps of correct simulation.

 An infinite recursion could be detected if a program comes back at the same place in the same state. In this case the beginning of D and the call to H are not the same place within the program. What Olcott means, but does not say, is that the call from D to H causes the program to arrive at a similar place in a similar state as when H (not D) started. But now we see that there are conditional branch instructions between these two places, namely within H, which may cause an end of the recursion. In fact, it is known that the recursion is not infinite, but does end, because H aborts and returns.

There are no conditional branch instructions that allow
the simulated D(D) to reach its own final state and halt.
In fact neither the simulated D(D) nor the executed H(D,D) can
possibly stop running unless the executed H(D,D) aborts its
simulation without waiting for any simulated H(D,D) to do this.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer