Re: Halting Problem is wrong two different ways

On 2024-06-06 13:48:29 +0000, olcott said:

On 6/6/2024 4:34 AM, Mikko wrote:

On 2024-06-05 13:18:24 +0000, olcott said:
 

On 6/5/2024 2:13 AM, Mikko wrote:

On 2024-06-04 17:40:47 +0000, olcott said:
 

On 6/4/2024 3:28 AM, Mikko wrote:

On 2024-06-03 18:14:39 +0000, olcott said:
 

On 6/3/2024 9:27 AM, Mikko wrote:

On 2024-06-03 12:20:01 +0000, olcott said:
 

On 6/3/2024 4:42 AM, Ben Bacarisse wrote:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
 

PO's D(D) halts, as illustrated in various traces that have been posted here.
PO's H(D,D) returns 0 : [NOT halting] also as illustrated in various traces.
i.e. exactly as the Linz proof claims.  PO has acknowledged both these
results.  Same for the HH/DD variants.
 You might imagine that's the end of the matter - PO failed.  :)
 That's right, but PO just carries on anyway!

 He has quite explicitly stated that false (0) is the correct result for
H(D,D) "even though D(D) halts".  I am mystified why anyone continues to
discuss the matter until he equally explicitly repudiates that claim.
 

 Deciders only compute the mapping *from their inputs* to their own
accept or reject state.

 That does not restrict what a problem statement can specify.
If the computed mapping differs from the specified one the
decider does not solve the problem.

 int sum(int x, int y) { return x + y; }
sum(2,3) cannot return the sum of 5 + 6.

 That does not restrict what a problem statement can specify.
If the mapping computed by sum differs from the specified one
the program sum does not solve the problem.
 

 On 6/3/2024 9:53 PM, Richard Damon wrote:
 > Because you keep on mentioning about DD Halting,
 > which IS about the direct execution of DD
 Only when one contradicts the definition of a decider that must
compute the mapping FROM ITS INPUTS BASED ON THE ACTUAL BEHAVIOR
OF THESE INPUTS (as measured by DD correctly simulated by HH).
 When we go ahead and contradict this definition then the
*HALTING PROBLEM IS STILL WRONG IN A DIFFERENT WAY*
 When D is defined to do the opposite of whatever yes/no
an answer that H provides then the counter-example input
is precisely isomorphic to the question:
Is this sentence: "This sentence is not true." true or false?
Thus that question and the HP question are both incorrect
because both yes and no are the wrong answer.
 The theory of computation may be ignorant of the details of
how the context of who is asked a question changes the meaning
of this question, none-the-less this cannot be ignored.
It is and remains incorrect for the theory of computation
to ignore this.

 Nice to see that you don't disagree with my observation that
your statement
 

Deciders only compute the mapping *from their inputs* to their own
accept or reject state.

 does not restrict what a problem statement can specify.
 

 Sure it does.
int sum(int x, int y) { return x + y; }
sum(3,4) cannot correctly return the sum of 5 + 6.

 That does not restrict what the problem statement can specify.
 

 When someone tries to prove that sum(3,4) is incorrect on the
basis that it cannot correctly provide the sum of 5 + 6, then
they are wrong.

Meybe, maybe not. That depends on the requirements. In any case,
that does not restrict what the problem statement can specify.
--
Mikko