Re: The Halting Problem is merely an erroneously formed question



Peter Olcott wrote:
On 2/12/2012 9:06 AM, Patricia Shanahan wrote:
I am not leaving out the input data. This is the input data:

if ( TheProgramHalts( String SourceCode ) )
Loop Forever;
else
Exit;

No, I meant the input data for the of SourceCode whose halting we are
testing. Remember SourceCode may represent a TM that halts for some
initial tape contents but halts for others.

// Converted the syntax from declaration to invocation
//
if ( TheProgramHalts( SourceCode ) )
Loop Forever;
else
Exit;

The Halting Problem is essentially that there can not possibly exist any possible implementation of the above referenced: bool TheProgramHalts(String SourceCode) that provides the correct Boolean result when the above program is provided as input to this bool TheProgramHalts(String SourceCode) halt analyzer.

YOU GOT IT!


Although the conclusion is true, it is only true because the above program forms invalid input to the halt analyzer.

It is a correctly formed halting question with an exact true/false
answer. There is no problem with the question unless you start out by
assuming that the TM we are testing is a valid halting decider.

Take another look at the earlier examples I posted of testing TMs that
always return true or always return false. I demonstrated there that
even when the TM we are testing gets the question wrong, another TM,
given the same question reports the correct true/false answer. That
would be impossible if the question had no right answer.

Patricia
.



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