Re: V5 --- Professor Sipser

On 2024-08-23 03:53:14 +0000, olcott said:

On 8/22/2024 10:11 PM, Richard Damon wrote:

On 8/22/24 10:54 PM, olcott wrote:

On 8/22/2024 9:31 PM, Richard Damon wrote:

On 8/22/24 9:39 PM, olcott wrote:

On 8/22/2024 8:26 PM, Richard Damon wrote:

On 8/22/24 9:21 PM, olcott wrote:

On 8/22/2024 7:54 PM, Richard Damon wrote:

On 8/22/24 9:36 AM, olcott wrote:

On 8/22/2024 8:21 AM, joes wrote:

Am Thu, 22 Aug 2024 07:59:59 -0500 schrieb olcott:

On 8/22/2024 3:16 AM, Fred. Zwarts wrote:

Op 22.aug.2024 om 06:22 schreef olcott:

 <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
      If simulating halt decider H correctly simulates its input D until
      H correctly determines that its simulated D would never stop
      running unless aborted then
      H can abort its simulation of D and correctly report that D
      specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
 We swap the word "determines" for "predicts"
When we swap thew word "halt decider" for "termination analyzer" the
above is translated from computer science into software engineering.
The second half proves that this is the H that aborts that is making the
prediction of the behavior of D when emulated by a hypothetical version
of itself then never aborts.

 

THIS EXACTLY MATCHES THE SIPSER APPROVED CRITERIA The finite HHH(DDD)
emulates itself emulating DDD exactly once and this is sufficient for
this HHH to predict what a different HHH(DDD) do that never aborted
its emulation of its input.

But that different hypothetical HHH is a non-input.

HHH is supposed to predict what the behavior of DDD would be if it did
not abort its emulation of DDD that is what the words that Professor
agreed to mean.

If IT didn’t abort DDD calling its aborting self.
 

 I don't know how you twist words to get that.
HHH is required to predict the behavior of DDD
as if every HHH had its abort code removed.

 But that isn't the input, so that is just a LIE.

 PREDICT HYPOTHETICAL BEHAVIOR

Nope, Predict the ACTUAL behavior.
 You are just admitting you are lying about the

 That is NOT what the words actually say.
I hope you don't get condemned to Hell over this.
 

 Yes, it is, at least when you understand the TECHNICAL meaning of the words in Computation Theory.

 Termination analyzers in software engineering are
isomorphic to partial halt deciders in computer
science you really can't get away with saying otherwise
and not look foolish.

 Then they must follow the same rules (or you are lying that they are isomoprhic).
 Deciders of program behavior must be given PROGRAMS, which always contain ALL of the code used by it, thus for DDD, it includes the HHH that it calls.
 

 It was ridiculous that you ever assumed otherwise.
 

Incomplete descriptions that just don't contain everything are just incorrect.
 Also, "Termination analyzers" are NOT the same thing as a Halt Deciders, as the term "Termination Analyzers" refer to something that decides if a given program will Halt on ALL POSSIBLE inputs, rather than the specific given input that a Halt Decider decides on.
 

 So you don't know what "isomorphic" means.
It does not mean identical in every respect.
Maybe "functionally equivalent" is easy for you.

Structurally equivalent is probably better.
U and U' are said to be isomorphic if there is a higher order bijection
that maps every constituent x of U to the corresponding constituent x'
of U' so every constituent of U' is mapped from some constitient of U,
every function f in U to a function f' in U' so that for every x
in U the bijection maps f(x) to f'(x'), and for every predicate P in U
there is a corresponding predicate P' in U' so that for every x in U
P(x) <-> P'(x'), as well as similar correspondences for functions and
predicates of several arguments.
An isomorfism between U and U is called an automorphism of U.
--
Mikko