On 10/29/2020 1:13 AM, Graham Cooper wrote:
> On Thursday, October 29, 2020 at 1:17:46 PM UTC+10, olcott wrote:
>> On 10/28/2020 9:44 PM, Graham Cooper wrote:
>>> what about Linz counter example ?
>>>
>>> loops(loops)
>>> if halt( loops loops) then loops(loops)
>>>
>>>
>>> if loops(loops) definitely halts what is the value of halt(loops,loops) ?
>>>
>> The RASP is a random-access machine (RAM) model that, unlike the RAM,
>> has its program in its "registers" together with its input. The
>> registers are unbounded (infinite in capacity); whether the number of
>> registers is finite is model-specific. Thus the RASP is to the RAM as
>> the Universal Turing machine is to the Turing machine. The RASP is an
>> example of the von Neumann architecture whereas the RAM is an example of
>> the Harvard architecture.
>>
>>
https://en.wikipedia.org/wiki/Random-access_stored-program_machine
>>
>> x86 language ≡ von Neumann architecture ≡ UTM ≡ RASP Machine
>>
>> I just completed one man-year's worth of work creating the x86utm
>> operating system that correctly decides the Linz counter-example as
>> non-halting.
>
>
> RIGHT! the counter-example doesn't halt
>
>
> loops(loops)
> if halt( loops loops)-X then loops(loops)
>
> halt doesn't return TRUE or FALSE though, it goes into an infinite loop at X
I spent a man year developing the x86utm operating system so that I
could show every single detailed step of exactly how and why the Linz
halt decider halts in its ((qn)) state.
x86 language ≡ von Neumann architecture ≡ UTM ≡ RASP Machine
The reason that a halt decider can actually decide that the Linz H_Hat
does not halt is based on the fact that it gets stuck in infinite
recursion before it ever reaches its undecidable states. We can tell
that it gets stuck in infinite recursion because it invokes the halt
decider a second time from the same machine address without any
conditional instructions in its execution trace in-between that would
terminate this otherwise infinite recursion. I derived this solution
2018-12-13 @ 7:00 PM.
--
Copyright 2020 Pete Olcott