On 5/28/2021 7:08 PM, olcott wrote:
> I spent two years creating the x86utm operating system to concretely
> address the halting problem using a halt decider written in C. This
> partial halt decider invokes an x86 emulator to execute the input in
> debug step mode. The input is the machine address of the x86 function.
>
> It examines the complete execution trace of this input immediately after
> each x86 instruction is simulated. As soon as the partial halt decider
> recognizes a non-terminating behavior pattern it aborts the simulation
> and reports not-halting.
>
> int D(u32 P)   // machine address of function
> {
>   if ( H(P, P) )
>     return 0   // reject when H accepts
>   return 1;    // accept when H rejects
> }
>
> When H is a simulating halt decider H(D,D) rejects its input as a
> halting computation on the basis that H(D,D) specifies infinitely nested
> simulation to H unless H aborts its simulation of D(D).
>
> *Table T   (All Turing machines on each other as input)*
>     <M1>     <M2>     <M3>...  <D>...
> M1  accept                     reject
> M2           reject            accept
> M3                    ~halt    accept
> ...
> D   reject   accept   accept   accept
> ...
>
> Table TH is defined on the basis of Table T where:
> (a) accept becomes accept   (b) reject becomes reject   (c) ~Halt
> becomes reject
>
> *Table TH   (Turing machine H on all Turing Machine pairs as input)*
>     <M1>     <M2>     <M3>...  <D>...
> M1  accept                     reject
> M2           reject            accept
> M3                    reject   accept
> ...
> D   reject   accept   accept   reject
> ...
>
> On the diagonal:  a TM is executed with its own TM description as input.
> Table TD only has a single input that reverses the value of the diagonal
> of table TH for each TM description on the horizontal axis of table TH.
>
> *Table TD (reverses H decision along the diagonal of table TH) *
>     <M1>     <M2> <M3>...  <D>...
>     reject   accept   accept   accept
>
> ***All of the above table values are correct. *
> All of the values in TD must be the opposite of the values of the TH
> diagonal is satisfied:
> (a) The reject value of table TH at element (D, <D>) is corresponds to
> the actual behavior of H(D,<D>).
> (b) The accept value of table T at element (D, <D>) is corresponds to
> the actual behavior of D(<D>) also shown at element <D> in table TD.
>
> Because the requirement that table TH have the same (accept / reject)
> value as table T directly contradicts the actual behavior of H(D,<D>)
> and D(<D>) we can toss out this requirement as erroneous.
> The above proof was apparently based on a proof nearly identical to the
> Sipser proof: http://www.liarparadox.org/Sipser_165_167_out.pdf
>
> --
> Copyright 2021 Pete Olcott
>
> "Great spirits have always encountered violent opposition from mediocre minds." Einstein
>

Refutation of Halting Problem Diagonalization Argument
DOI: 10.13140/RG.2.2.34446.28483

https://www.researchgate.net/publication/351947980_Refutation_of_Halting_Problem_Diagonalization_Argument

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein