Re: HP counter-example INPUT cannot possibly exist

On 2025-06-21 15:49:30 +0000, olcott said:

On 6/21/2025 3:20 AM, Mikko wrote:

On 2025-06-20 16:54:32 +0000, olcott said:
 

On 6/19/2025 3:17 AM, Mikko wrote:

On 2025-06-18 16:05:33 +0000, olcott said:
 

On 6/18/2025 10:57 AM, joes wrote:

Am Wed, 18 Jun 2025 09:39:02 -0500 schrieb olcott:

On 6/16/2025 3:21 AM, Mikko wrote:

On 2025-06-15 14:44:47 +0000, olcott said:

On 6/15/2025 4:19 AM, Mikko wrote:

On 2025-06-13 15:33:45 +0000, olcott said:

On 6/13/2025 5:37 AM, Mikko wrote:

 

As you respond to my question without answering it it is obvious
that you don't see any proofs in your article.

 It is a fact that there is no actual input D to any termination
analyzer H that does the opposite of whatever value that H derives.
The key element that all conventional HP proofs depend on cannot
possibly exist.

 Nonsense is not a fact.

 After studying these things for 22 years I found that every
conventional proof of the halting problem never provides an actual
input that would do the opposite of whatever value that its partial
halt decider (PHD) returns.

 The core part of those proofs is a constructive specification of that
test case.
 

Yet no one ever noticed that the counter-example input cannot even be
constructed thus the proof itself never actually existed.

In what sense? The code for DDD is clearly in your repository.

 There has never been any HP proof that has
ever defined *AN ACTUAL INPUT* to a termination
analyzer that can possibly do the opposite of
whatever value that this termination analyzer
determines.

 Of course a proof of the halting problem does not define anything
for a termination alayzer. Termination anlyzers are not a relevant
for any proof (or other discussion) about the halting problem.
 

 Simulating termination analyzer are equivalent to
a partial halt deciders.

 If they are they should be called "simulating partial halt deciders".

 That is too confusing for most of my reviewers.

It is long but there is no evdence that it would be confusing. Those
whose opinion is worth of attention know what "decider" means and
what "halt decider means" and what "partial" means in this context,
and they interprete the word "simulating" to mean that the algorithm
involves simulation. If more clarification is needed you are free to
write more clearly.

Simulating termination analyzer is an existing
term with the exact meaning that I am referring to.

No, it is not. The exact meaning of "termination analyzer" means an
analyzer that can analyze programs that take an input. Programs that
don't take an input are an uninteresting marginal case. The word
"simulating" does not affect that aspect of the meaning.

The term "termination analyzer" refers to a problem different from
the halting problem.

 Not at all.
Google [termination analyzer versus halt decider]

Googel does not find anyting authoritative with those words.

The halting problem is about questions about computations but
the termination problem is about questions about programs.

 In both cases the STA or the SPHD is required to determine
the behavior specified by the *input* encoded as a sequence
of state changes.

No, a sequence of state changes is not required. Both require some
description of an algorithm but an exact definition of state space
and state changes is not required. A partial halt decider takes the
same input as an universal Turing machine: an input that contains
a description of an algrithm and a descrition of an input to that
algorithm. Only if the decider is restricted to computations that
all have the same input (e.g., empty tape) the description of the
input is not needed. Conseqently, the meaning of "behaviour" is
different for the two kinds of programs. For a partial halting
decider it means what the algorithm specified by the input to the
decider does with the input specified by the input to the decider.
For a termination analyzer it means anything the algorithm specified
by the input may do with any input it can be given. In both cases
only one aspect of behaviour is required to be determined. For a
halt decider it is whether the algorithm terminates with the
specified input, for a termination analyzer it is whether the
algorithm terminates with every possible input. The definitions
neither require nor prohibit any other output.
--
Mikko