whether >>>>     TM P run with input I on its input tape halts. >>>>     [

is the string representation of the actual TM P, and >>>>      is the string representation of input tape I] >>>> -  Construct from H a new TM H^ using the mechanical process described in the proof. >>>>     If H exists, then its corresponding H^ also exists. >>>> -  Show that the construction of H^ ensures that: >>>>     -  if H decides input (representing H^ running with input ) halts, >>>>        then that implies that H^ running with input never halts >>>>     -  if H decides input never halts, >>>>        then that implies H^ running with input halts >>>>     I.e. either way, H decides the specific input incorrectly, contradicting >>>>     the initial assumption that H is a halt decider. >>>> -  So no halt decider exists.  (Every proposed halt decider decides at least one input case >>>>     incorrectly, viz input .) >>>> >>>> PO basically claimed he had a fully coded TM H, which CORRECTLY decides its "nemesis" input >>>> , contradicting the logic of the Linz proof [without pointing out any actual mistake in >>>> the Linz proof].  Given most people here understand the Linz proof well enough to see it is >>>> basically sound, people were sceptical! >>>> >>>> It turned out PO was lying about the fully coded TM, and in fact what he actually had was the >>>> idea behind a C program which would "prove" his idea.  A couple of years(?) later he actually >>>> completed his C program and his x86utm.exe which would simulate the x86 code of his H and H^ to >>>> "prove" his claim.  His equivalent of Linz H is his C function H or HH, and his equivalent of >>>> Linz H^ is his D or DD respectively.  (They run under x86utm.exe and are not Windows/Unix >>>> executables.) >>>> >>>> H/HH use PARTIAL simulation of their input to decide halting/non-halting, returning >>>> 0 or 1 to communicate their decision.  As you correctly point out, to the HP proof simulation is >>>> quite irrelevant, being just one kind of data manipulation that H may perform on its input >>>> string

before it decides the halting status.  So the Linz HP proof covers such H, no >>>> problem. >>>> [I put PARTIAL in caps, just because there seems to be some confusion in recent threads as to >>>> what PO means by "simulation".  He doesn't say it explicitly, despite suggestions to this >>>> effect, but he always means what might be called /partial/ simulation.] >>>> >>>> PO believes that by (partially) simulating the computation corresponding to the input

>>>> [i.e. calculating the successive x86 instruction steps of the computation P(I)] and monitoring >>>> the progress of virtual x86 state changes (like instruction address and op-code and so on) H >>>> could spot some pattern that reveals whether computation P(I) halts or not.  At this point in >>>> the partial simulation, his H would stop simulating (aka "abort" the simulation) and return the >>>> appropriate halt status for input

. >>>> >>>> Nothing remarkable so far!  Clearly a tight-loop in P /can/ be detected in this fashion, so >>>> /some/

inputs /can/ be correctly determined like this.  The PO claim however is that the >>>> specific input is correctly decided by his H.  In C terms those correspond to H(D,D) >>>> correctly returning the halt status of computation D(D).  [PO would probably dispute this, >>>> because he doesn't properly understand halting or the HP generally, or in fact pretty much /any >>>> abstract concept/ ] >>>> >>> >>> Introduction to the Theory of Computation, by Michael Sipser >>> https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X/ >>> >>> On 10/13/2022 11:29:23 AM >>> MIT Professor Michael Sipser agreed this verbatim paragraph is correct >>> (He has neither reviewed nor agreed to anything else in this paper) >>> >>> >>> If simulating halt decider H correctly simulates its input D until H >>> correctly determines that its simulated D would never stop running >>> unless aborted then >>> >>> H can abort its simulation of D and correctly report that D specifies a >>> non-halting sequence of configurations. >>> >>> >>> I have started working on what seem to be some computability issues >>> that you pointed out with my HH. I found that they are isolated to >>> one single element of HH. Essentially the details of how the master >>> UTM directly executed HH passes a portion of its tape to its slaves. >>> >>> Nothing else seems to have any computability issues by the measure >>> that I am using. >>> >>> Message-ID: >>> On 3/1/2024 12:41 PM, Mike Terry wrote: >>>  > >>>  > Obviously a simulator has access to the internal state >>>  > (tape contents etc.) of the simulated machine. No problem there. >>> >>> Because of your above comment it seems that correcting this >>> tiny computability issue with HH is my best path forward. >>> >>> >>> >>> >>> You have given the following a blatantly false review when I >>> said the same thing another way: >> >> I have no idea what you're talking about.  I did not write any of what follows below. >> >> Also I don't believe I said anything "blatantly false".  You're incapable of judging what other >> people say or are thinking - you're often telling people that they'er lying to you and denying >> "previously verified facts" etc. but its all rubbish - you're in no position to make such judgements. >> >> >> Mike. >> > > You said that the execution trace that I proved is correct is > incorrect because you didn't like the way that HH was written. > You said this without looking at my proof as you are doing > here again. An execution trace that is produced by a program that is incorrect /proves/ nothing whatsoever. I don't need to look at your proof, as I was commenting on the value of your program output AS PROOF. It's like you claim you are going to write a program that proves that the sum of integers 1 to 10 is 55, and here is your program source and the output: source: int main () { int total = 0; for (int x = 3; x <= 10; x++) // look carefully at the range for the loop total += x; end; printf ("Sum of integers from 1 to 10 is: %d\n", 55); } output: Sum of integers from 1 to 10 is: 55 Well the output is correct! And my program proved it, because it wrote a true statement!! (Um, No. Given my program output is incorrect, it proves nothing. Similarly if your program does not correctly simulate computation DD(DD) [WHICH IT DEFINITELY DOESN'T BECAUSE IT'S SIMULATION OF HH IS NONSENSE DUE TO MISUSE OF GLOBALS IN DD ETC.] there's no point in you trying to claim that it's trace is correct despite the program being wrong. The point is correct or not, the trace PROVES nothing, like my output above. Duh. This whole situation mirrors your lack of understanding what a proof is. For you a proof is just making lots of claims you think are true (aka your intuitions) perhaps with the rule that the last thing you claim must be whatever you're claiming. And it's not a case of simply "disliking the way HH is written" which trivialises the problem - like I'm objecting to your naming conventions or something. Your HH is completely wrong in its implementation of simulation - like my program above is wrong in its calculation, regardless of what it outputs. HH does not actually simulate itself correctly AT ALL. > >> >>> >>> *We can see that the following DD cannot possibly halt when* >>> *correctly simulated by every HH that can possibly exist* ... and I don't believe I even commented on the correctness or otherwise for that claim. Mike. >>> >>> typedef int (*ptr)();  // ptr is pointer to int function in C >>> 00       int HH(ptr p, ptr i); >>> 01       int DD(ptr p) >>> 02       { ========== REMAINDER OF ARTICLE TRUNCATED ==========