Quote:
Originally Posted by Buffy
No, that is an assumption on your part!
Determining the termination of a program can proceed by a deconstruction of the logical structure of the code itself. Or do you have some reason to insist that this is not a possible approach to constructing a Halting Program? If you have no evidence or theory to back up this assertion, its simply an unsupported assumption on your part.
There is nothing in the theorem that requires tracing whatsoever: again you tar the theory for doing exactly what you insist on doing to disprove it!
Not everything that is faced can be changed, but nothing can be changed until it is faced, 
Buffy |
The only part of that the proof does not explicitly state is the part about tracing the computations. So we are left to wonder how on earth the Halting Machine would operate without tracing the input machine.
But that is irrelevant, and I need not prove that a proposed Halting Machine H such as that in the proof would involve tracing computations. Touring Assumes it doesn't in his proof by contradiction, thus provided the more likely source of the contradiction he derives.
So to recap, the things touring assumes to start with are:
There exists an H
H retains its normal function when operated as part of the constructed machine which is given itself as input.
and by logical consequence of that assumption
H does not trace computations of machines input into it, since doing so in the constructed composite machine would cause an infinite regress that would cease the machines normal function. IE such a machine is outside of it's own domain.
And also many other trivial things or things that he has previously proven that allow him to construct his argument.
These second and third assumptions are by no means trivial, which means he cannot reasonably say that there is no such H upon reaching the contradiction.
