On 3/16/25 2:05 PM, olcott wrote:
On 3/16/2025 12:38 PM, dbush wrote:
On 3/16/2025 1:18 PM, olcott wrote:
On 3/16/2025 11:54 AM, Richard Heathfield wrote:
On 16/03/2025 16:46, dbush wrote:
A solution to the halting problem is an algorithm H
And therefore, according to Knuth, the solution has the following
properties:
Finiteness - An algorithm must start and stop. The rules an
algorithm applies must also conclude in a reasonable amount of time.
What “reasonable” is depends on the nature of the algorithm, but in >>>> no case can an algorithm take an infinite amount of time to complete
its task. Knuth calls this property the finiteness of an algorithm.
Definiteness - The actions that an algorithm performs cannot be open
to multiple interpretations; each step must be precise and
unambiguous. Knuth terms this quality definiteness. An algorithm
cannot iterate a “bunch” of times. The number of times must be
precisely expressed, for example 2, 1000000, or a randomly chosen
number.
Inputs - An algorithm starts its computation from an initial state.
This state may be expressed as input values given to the algorithm
before it starts.
The direct execution of DD() IS NOT AN INPUT VALUE TO HHH.
It is when the requirements say so:
That is not the way that reality works.
Dogma that disagrees with truth is incorrect.
A static finite string <is not> a dynamic process.
That *IS* the way reality works.
You just don't understand what is real, as you live in a world of
make-beleive where the Truth Fairy makes what ever you want to be true
to be true.
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