Re: Turing computable functions

On 3/25/2025 2:32 PM, dbush wrote:

On 3/25/2025 3:24 PM, olcott wrote:

Cannot possibly derive any outputs not computed from
their inputs.

 Correct, algorithms can only compute computable mathematical function.
 

>
A Turing machine halt decider

 Does not exist because the required mapping is not computable:
  Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
 A solution to the halting problem is an algorithm H that computes the following mapping:
 (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
  

cannot possibly report
on the behavior of any directly executing process.
No Turing machine can every do this. This has always
been beyond what any Turing machine can ever do.

  Strawman: reporting on an executing process is not a requirement.

YOU JUST SAID THAT IT WAS
YOU KEEP MINDLESSLY REPEATING THAT IT IS
On 3/25/2025 2:32 PM, dbush wrote:
 > (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer