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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Incorrect requirements --- Computing the mapping from the input
 to HHH(DD)
Date: Sun, 11 May 2025 00:00:48 +0800
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On Sat, 2025-05-10 at 10:43 -0500, olcott wrote:
> On 5/10/2025 10:14 AM, wij wrote:
> > On Sat, 2025-05-10 at 09:51 -0500, olcott wrote:
> > > On 5/10/2025 1:19 AM, wij wrote:
> > > > On Sat, 2025-05-10 at 01:06 -0500, olcott wrote:
> > > > > On 5/10/2025 1:00 AM, wij wrote:
> > > > > > On Sat, 2025-05-10 at 00:41 -0500, olcott wrote:
> > > > > > > On 5/10/2025 12:27 AM, wij wrote:
> > > > > > > > On Sat, 2025-05-10 at 00:19 -0500, olcott wrote:
> > > > > > > > > On 5/10/2025 12:13 AM, wij wrote:
> > > > > > > > > > On Sat, 2025-05-10 at 00:06 -0500, olcott wrote:>>
> > > > > > > > > > > When mathematical mapping is properly understood
> > > > > > > > > > > it will be known that functions computed by models
> > > > > > > > > > > of computation must transform their input into
> > > > > > > > > > > outputs according to the specific steps of an
> > > > > > > > > > > algorithm.
> > > > > > > > > > >=20
> > > > > > > > > > > _DDD()
> > > > > > > > > > > [00002172] 55=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0 push ebp=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 ; housekeeping
> > > > > > > > > > > [00002173] 8bec=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 m=
ov ebp,esp=C2=A0=C2=A0 ; housekeeping
> > > > > > > > > > > [00002175] 6872210000 push 00002172 ; push DDD
> > > > > > > > > > > [0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
> > > > > > > > > > > [0000217f] 83c404=C2=A0=C2=A0=C2=A0=C2=A0 add esp,+04
> > > > > > > > > > > [00002182] 5d=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0 pop ebp
> > > > > > > > > > > [00002183] c3=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0 ret
> > > > > > > > > > > Size in bytes:(0018) [00002183]
> > > > > > > > > > >=20
> > > > > > > > > > > For example HHH(DDD) only correctly map to the
> > > > > > > > > > > behavior that its input actually specifies by correct=
ly
> > > > > > > > > > > emulating DDD according to the rules of the x86 langu=
age.
> > > > > > > > > > >=20
> > > > > > > > > > > This causes the first four instructions of DDD
> > > > > > > > > > > to be emulated followed by HHH emulating itself
> > > > > > > > > > > emulating the first three instructions of DDD.
> > > > > > > > > > >=20
> > > > > > > > > > > It is right at this recursive simulation just
> > > > > > > > > > > before HHH(DDD) is called again that HHH recognizes
> > > > > > > > > > > the repeating pattern and rejects DDD.
> > > > > > > > > >=20
> > > > > > > > > > Yes, but you still did not answer the question: Is POOH=
 exactly about HP?
> > > > > > > > > >=20
> > > > > > > > >=20
> > > > > > > > > =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0>>>>> H(D)=3D1 if D() halt.
> > > > > > > > > =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0>>>>> H(D)=3D0 if D() not h=
alt.
> > > > > > > > >=20
> > > > > > > > > Right now it is mostly about proving the
> > > > > > > > > above requirements are is mistaken.
> > > > > > > > >=20
> > > > > > > >=20
> > > > > > > > Why is the requirement invalid?
> > > > > > > >=20
> > > > > > > > H(D)=3D1 if D() halt.
> > > > > > > > H(D)=3D0 if D() not halt.
> > > > > > > >=20
> > > > > > >=20
> > > > > >=20
> > > > > > > The notion that the behavior specified by the finite
> > > > > > > string input to a simulating termination analyzer
> > > > > >=20
> > > > > > POOH reads(takes) its input as a function, not 'finite string'.
> > > > > > Are you talking about POOH now? There is no POOH that takes
> > > > > > 'finite string'.
> > > > > >=20
> > > > >=20
> > > > > It <is> a finite string of x86 bytes.
> > > >=20
> > > > Disagree.
> > > > The D in Halt7.c (I just saw once) does not treat H as 'finite stri=
ng',
> > > > D calls H. H also does not treat D as 'finite string'.
> > > >=20
> > >=20
> > > HHH and DDD and DD are the most recent functions.
> > > HHH does emulate its finite strings of x86 machine code
> > > according to the rules of the x86 language.
> >=20
> > This is from a copy of Halt7.c:
> >=20
> > void P(ptr x)
> > {
> > =C2=A0=C2=A0 int Halt_Status =3D H(x, x);
> > =C2=A0=C2=A0 if (Halt_Status)
> > =C2=A0=C2=A0=C2=A0=C2=A0 HERE: goto HERE;
> > =C2=A0=C2=A0 return;
> > }
> >=20
> > int main()
> > {
> > =C2=A0=C2=A0 Output("Input_Halts =3D ", H(P, P));
> > }
> >=20
> > H reads a *pointer*.
> > In P, P *calls* H.
> >=20
> > Both do not process 'finite string'.
> >=20
>=20
> What it is it a pointer to a box of chocolates?
> finite strings are passed as pointers to finite
> string in C.

Nope. I don't believe it is a pointer to chocolates, even if you say so.
It is about the code of D/H itself. They do not process string, the fact sa=
ys
the author of the program does not intend to process 'string'.

> > > > > > > does sometimes differ from the behavior of its direct
> > > > > > > execution. It is a provably different sequence of steps.
> > > > > >=20
> > > > >=20
> > > > > This is a verified fact.
> > > > > The pathological relationship that inputs can have
> > > > > with their simulating termination analyzer changes
> > > > > the behavior of these inputs relative to their direct
> > > > > execution.
> > > >=20
> > > > So, you redefined the halting problem should be about the behavior =
of D
> > > > decided by POOH, not the 'direct' behavior of D?
> > > >=20
> > >=20
> > > Not at all. HHH(DDD) reports on the behavior that DDD
> > > actually specifies. All my critics require HHH to report
> > > on behavior that DDD does not actually specify.
> > >=20
> > > The actual behavior that DDD specifies is measured
> > > by HHH emulating DDD according to the rules of the
> > > x86 language. My critics insist on ignoring these
> > > rules because it does not derive the behavior that
> > > they expect.
> >=20
> > =C2=A0From this reply and others before. Can we conclude that POOH is
> > about the pathological relationship inputs to the halting decider H.
> > IOW, POOH computes the function: POOH(D)=3D1 iff D is pathological.
> >=20
> > POOH is not about the 'incorrect' problem HP: POOH(D)=3D1 iff D() halt?
> >=20
>=20
> Once we have the extra detail about how models
> of computation computing functions must compute
> the mapping from their actual inputs to the
> behaviors that these inputs actually specify
>=20
> then we can see that I corrected a mistake in
> the theory of computation.

What is the theory of computation? HP?

> > > I proved that these expectations are incorrect.
> > >=20
> > > int sum(int x, int y) { return x + y ;}
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