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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Can D simulated by H terminate normally? --- Message_ID Provided
Date: Mon, 20 May 2024 20:57:39 -0400
Organization: i2pn2 (i2pn.org)
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On 5/20/24 2:17 PM, olcott wrote:
> On 5/20/2024 6:24 AM, Richard Damon wrote:
>> On 5/20/24 1:17 AM, olcott wrote:
>>> On 5/19/2024 11:37 PM, immibis wrote:
>>>> On 19/05/24 15:06, olcott wrote:
>>>>> On 5/19/2024 7:16 AM, immibis wrote:
>>>>>> On 19/05/24 05:59, olcott wrote:
>>>>>>> On 5/18/2024 6:38 PM, Richard Damon wrote:
>>>>>>>> On 5/18/24 7:24 PM, olcott wrote:
>>>>>>>>> On 5/18/2024 6:06 PM, Richard Damon wrote:
>>>>>>>>>> On 5/18/24 6:44 PM, olcott wrote:
>>>>>>>>>>> On 5/18/2024 3:02 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/18/24 3:57 PM, olcott wrote:
>>>>>>>>>>>>> On 5/1/2024 7:10 PM, Richard Damon wrote:
>>>>>>>>>>>>>> The second method uses the fact that you have not 
>>>>>>>>>>>>>> restricted what H is allowed to do, and thus H can 
>>>>>>>>>>>>>> remember that it is simulating, and if a call to H shows 
>>>>>>>>>>>>>> that it is currently doing a simulation, just immediately 
>>>>>>>>>>>>>> return 0. 
>>>>>>>>>>>>>
>>>>>>>>>>>>> Nice try but this has no effect on any D correctly 
>>>>>>>>>>>>> simulated by H.
>>>>>>>>>>>>> When the directly executed H aborts its simulation it only 
>>>>>>>>>>>>> returns
>>>>>>>>>>>>> to whatever directly executed it.
>>>>>>>>>>>>
>>>>>>>>>>>> Why? My H does correctly simulate the D it was given.
>>>>>>>>>>>>
>>>>>>>>>>>> You don't seem to understand how the C code actually works.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> If the directly executed outermost H does not abort then 
>>>>>>>>>>>>> none of
>>>>>>>>>>>>> the inner simulated ones abort because they are the exact 
>>>>>>>>>>>>> same code.
>>>>>>>>>>>>> When the directly executed outermost H does abort it can 
>>>>>>>>>>>>> only return
>>>>>>>>>>>>> to its own caller.
>>>>>>>>>>>>
>>>>>>>>>>>> WHAT inner simulatioin?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> My H begins as:
>>>>>>>>>>>>
>>>>>>>>>>>> int H(ptr x, ptr y) {
>>>>>>>>>>>>    static int flag = 0;
>>>>>>>>>>>>    if(flag) return 0;
>>>>>>>>>>>>    flag = 1;
>>>>>>>>>>>>
>>>>>>>>>>>> followed by essentially your code for H, except that you 
>>>>>>>>>>>> need to disable the hack that doesn't simulate the call to 
>>>>>>>>>>>> H, but just let it continue into H where it will immediately 
>>>>>>>>>>>> return to D and D will then return.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Thus, your claim is shown to be wrong.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> We are talking about every element of an infinite set where
>>>>>>>>>>> H correctly simulates 1 to ∞ steps of D thus including 0 to ∞
>>>>>>>>>>> recursive simulations of H simulating itself simulating D.
>>>>>>>>>>>
>>>>>>>>>>> *At whatever point the directly executed H(D,D) stops 
>>>>>>>>>>> simulating*
>>>>>>>>>>> *its input it cannot possibly return to any simulated input*
>>>>>>>>>>
>>>>>>>>>> And my H never stops simulating, so that doesn't apply. It 
>>>>>>>>>> will reach the final state.
>>>>>>>>>
>>>>>>>>> *Show the error in my execution trace that I empirically*
>>>>>>>>> *proved has no error by H correctly simulating D to the*
>>>>>>>>> *point where H correctly simulates itself simulating D*
>>>>>>>>> (Fully operational empirically code proved this)
>>>>>>>>
>>>>>>>> See below:
>>>>>>>>
>>>>>>>>
>>>>>>>>>
>>>>>>>>> typedef int (*ptr)();  // ptr is pointer to int function
>>>>>>>>> 00 int H(ptr x, ptr y);
>>>>>>>>> 01 int D(ptr x)
>>>>>>>>> 02 {
>>>>>>>>> 03   int Halt_Status = H(x, x);
>>>>>>>>> 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 }
>>>>>>>>
>>>>>>>> For Reference
>>>>>>>>
>>>>>>>> 14 int H(ptr x, ptr y)
>>>>>>>> 15 {
>>>>>>>> 16   static int flag = 0
>>>>>>>> 17   if (flag)
>>>>>>>> 18      return 0
>>>>>>>> 19   ... continuation of H that simulates its input
>>>>>>>>
>>>>>>>>>
>>>>>>>>> In the above case a simulator is an x86 emulator that correctly
>>>>>>>>> emulates at least one of the x86 instructions of D in the order
>>>>>>>>> specified by the x86 instructions of D.
>>>>>>>>>
>>>>>>>>> This may include correctly emulating the x86 instructions of H
>>>>>>>>> in the order specified by the x86 instructions of H thus calling
>>>>>>>>> H(D,D) in recursive simulation.
>>>>>>>>>
>>>>>>>>> Execution Trace
>>>>>>>>> Line 11: main() invokes H(D,D);
>>>>>>>>>
>>>>>>>>> keeps repeating (unless aborted)
>>>>>>>>> Line 01
>>>>>>>>> Line 02
>>>>>>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates 
>>>>>>>>> D(D)
>>>>>>>>
>>>>>>>> Line 03: Calls H (line 14)
>>>>>>>> Line 16: Static already inited, so not changed.
>>>>>>>> Line 17: Flag is 1, so
>>>>>>>> Line 18: Return 0
>>>>>>>> Line 03: Set Halt_Status to 0
>>>>>>>> Line 04: if (Halt_Status)      halts status is 0, so skip
>>>>>>>> Line 06: return Halt_Status
>>>>>>>>
>>>>>>>> Simulation completed, program halted.
>>>>>>>>
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Simulation invariant:
>>>>>>>>> D correctly simulated by H cannot possibly reach past its own 
>>>>>>>>> line 03.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Nope. Not for this H
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> (a) That idea might work yet you did not say it correctly.
>>>>>>> For example line 11 is the first one invoked.
>>>>>>> (b) Computable functions cannot alter their behavior this way.
>>>>>>>
>>>>>>> (1) the function return values are identical for identical 
>>>>>>> arguments (no
>>>>>>> variation with local static variables, non-local variables, mutable
>>>>>>> reference arguments or input streams, i.e., referential 
>>>>>>> transparency), and
>>>>>>
>>>>>> Your function H works like Richard's function H. You just called 
>>>>>> the variable "execution trace" instead of "flag".
>>>>>
>>>>> pages 4-5 (of a paper that I published 2021-09-26 09:39 AM)
>>>>> Show H simulating P and H simulating itself simulating P.
>>>>>
>>>>> The 395 pages of the execution trace of the simulated H are
>>>>> screened out. No one here could ever understand the half page
>>>>> trace so embedding that in 395 more pages would not help.
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