Hi!
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider". It is a Partial Halt Decider over the domain of all *finite* program-input pairs excluding pathological input (a manifestation of the self referencial category error).
It is a Simulating Halt Decider with *infinite resources*.
Turing’s statement of the problem included logically invalid inputs. Once we correct the domain to disallow self-reference, the rest (of *finite*
size) are decidable.
/Flibble
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you haven't "created" a term, but just the idea of a term that you can't yet figure out how to define (and my guess is actually definable without
just loosing Turing Completeness of your system as even an idea you get
close to).
On 4/18/25 2:45 PM, Mr Flibble wrote:
Hi!
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider". It is a Partial Halt Decider over the domain
of all *finite* program-input pairs excluding pathological input (a
manifestation of the self referencial category error).
It is a Simulating Halt Decider with *infinite resources*.
Turing’s statement of the problem included logically invalid inputs.
Once we correct the domain to disallow self-reference, the rest (of
*finite* size) are decidable.
/Flibble
If you are trying to say that you machine with infinite resources can
decide on an input that can only use finite resources (that your
definition of a "finite program" is that it has a finite total storage
space) then this is a solved problem from generations before. The
"geared" simulation system, with two simulators, one running two steps
to the others one step, and looking for duplicated state, was well know
known decades ago, and doesn't need unbounded storage, just finite
storage, the two simulators of the finite machines, and what it takes to compare their state.
If you allow your input to represent actual Turing Equivalent machines,
which have finite program state, but unlimited tape storage, then you
haven't shown how you decide on them.
You also haven't shown how the inputs you want to exclude are "logically invalid". They may not be "decided" on by the given halt decider, but
there is nothing "invalid" about them, once you actually require your
decider to be a PROGRAM, and thus fixed and defined code.
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you haven't "created" a term, but just the idea of a term that you can't yet figure out how to define (and my guess is actually definable without
just loosing Turing Completeness of your system as even an idea you get
close to).
On Fri, 18 Apr 2025 15:00:10 -0400, Richard Damon wrote:
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you
haven't "created" a term, but just the idea of a term that you can't yet
figure out how to define (and my guess is actually definable without
just loosing Turing Completeness of your system as even an idea you get
close to).
Turing Completeness doesn't apply when we are dealing with logically
unsound category errors.
/Flibble
On Fri, 18 Apr 2025 15:00:10 -0400, Richard Damon wrote:
On 4/18/25 2:45 PM, Mr Flibble wrote:
Hi!
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider". It is a Partial Halt Decider over the domain
of all *finite* program-input pairs excluding pathological input (a
manifestation of the self referencial category error).
It is a Simulating Halt Decider with *infinite resources*.
Turing’s statement of the problem included logically invalid inputs.
Once we correct the domain to disallow self-reference, the rest (of
*finite* size) are decidable.
/Flibble
If you are trying to say that you machine with infinite resources can
decide on an input that can only use finite resources (that your
definition of a "finite program" is that it has a finite total storage
space) then this is a solved problem from generations before. The
"geared" simulation system, with two simulators, one running two steps
to the others one step, and looking for duplicated state, was well know
known decades ago, and doesn't need unbounded storage, just finite
storage, the two simulators of the finite machines, and what it takes to
compare their state.
If you allow your input to represent actual Turing Equivalent machines,
which have finite program state, but unlimited tape storage, then you
haven't shown how you decide on them.
You also haven't shown how the inputs you want to exclude are "logically
invalid". They may not be "decided" on by the given halt decider, but
there is nothing "invalid" about them, once you actually require your
decider to be a PROGRAM, and thus fixed and defined code.
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you
haven't "created" a term, but just the idea of a term that you can't yet
figure out how to define (and my guess is actually definable without
just loosing Turing Completeness of your system as even an idea you get
close to).
Flibble's Law (also known as The Principle of Computational Reciprocity):
If a problem permits infinite behavior in its formulation, it permits infinite analysis of that behavior in its decidability scope.
/Flibble
On 4/18/25 3:05 PM, Mr Flibble wrote:
On Fri, 18 Apr 2025 15:00:10 -0400, Richard Damon wrote:
On 4/18/25 2:45 PM, Mr Flibble wrote:
Hi!
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider". It is a Partial Halt Decider over the
domain of all *finite* program-input pairs excluding pathological
input (a manifestation of the self referencial category error).
It is a Simulating Halt Decider with *infinite resources*.
Turing’s statement of the problem included logically invalid inputs. >>>> Once we correct the domain to disallow self-reference, the rest (of
*finite* size) are decidable.
/Flibble
If you are trying to say that you machine with infinite resources can
decide on an input that can only use finite resources (that your
definition of a "finite program" is that it has a finite total storage
space) then this is a solved problem from generations before. The
"geared" simulation system, with two simulators, one running two steps
to the others one step, and looking for duplicated state, was well
know known decades ago, and doesn't need unbounded storage, just
finite storage, the two simulators of the finite machines, and what it
takes to compare their state.
If you allow your input to represent actual Turing Equivalent
machines, which have finite program state, but unlimited tape storage,
then you haven't shown how you decide on them.
You also haven't shown how the inputs you want to exclude are
"logically invalid". They may not be "decided" on by the given halt
decider, but there is nothing "invalid" about them, once you actually
require your decider to be a PROGRAM, and thus fixed and defined code.
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you
haven't "created" a term, but just the idea of a term that you can't
yet figure out how to define (and my guess is actually definable
without just loosing Turing Completeness of your system as even an
idea you get close to).
Flibble's Law (also known as The Principle of Computational
Reciprocity):
If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.
/Flibble
No it doesn't. You may think it should, but to meet the actual
requirements to provide the required knowledge it can't.
The fact that it might require infinite analysis became the answer to
the question, that some things are just not knowable, which was the big question at the time, could mathematics create a method to answer all questions, and the result was a clear NO, as mathematics allows us to
create problems with unknowable answers.
And the rules of the game are that deciders must answer in finite time.
On Fri, 18 Apr 2025 17:04:43 -0400, Richard Damon wrote:
On 4/18/25 3:05 PM, Mr Flibble wrote:
On Fri, 18 Apr 2025 15:00:10 -0400, Richard Damon wrote:
On 4/18/25 2:45 PM, Mr Flibble wrote:
Hi!
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider". It is a Partial Halt Decider over the
domain of all *finite* program-input pairs excluding pathological
input (a manifestation of the self referencial category error).
It is a Simulating Halt Decider with *infinite resources*.
Turing’s statement of the problem included logically invalid inputs. >>>>> Once we correct the domain to disallow self-reference, the rest (of
*finite* size) are decidable.
/Flibble
If you are trying to say that you machine with infinite resources can
decide on an input that can only use finite resources (that your
definition of a "finite program" is that it has a finite total storage >>>> space) then this is a solved problem from generations before. The
"geared" simulation system, with two simulators, one running two steps >>>> to the others one step, and looking for duplicated state, was well
know known decades ago, and doesn't need unbounded storage, just
finite storage, the two simulators of the finite machines, and what it >>>> takes to compare their state.
If you allow your input to represent actual Turing Equivalent
machines, which have finite program state, but unlimited tape storage, >>>> then you haven't shown how you decide on them.
You also haven't shown how the inputs you want to exclude are
"logically invalid". They may not be "decided" on by the given halt
decider, but there is nothing "invalid" about them, once you actually
require your decider to be a PROGRAM, and thus fixed and defined code. >>>>
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you >>>> haven't "created" a term, but just the idea of a term that you can't
yet figure out how to define (and my guess is actually definable
without just loosing Turing Completeness of your system as even an
idea you get close to).
Flibble's Law (also known as The Principle of Computational
Reciprocity):
If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.
/Flibble
No it doesn't. You may think it should, but to meet the actual
requirements to provide the required knowledge it can't.
The fact that it might require infinite analysis became the answer to
the question, that some things are just not knowable, which was the big
question at the time, could mathematics create a method to answer all
questions, and the result was a clear NO, as mathematics allows us to
create problems with unknowable answers.
Yes it does. Again:
It is about playing the game by the rules of the game:
If Busy Beavers are allowed an INFINITE tape in the context of the Halting Problem then Simulating Halt Deciders are allowed INFINITE resources.
/Flibble
On Fri, 18 Apr 2025 17:15:40 -0400, Richard Damon wrote:
And the rules of the game are that deciders must answer in finite time.
Your perspective is:
Epistemic: knowledge must be actionable, and thus based on finite computation.
Pragmatic: we need results in time, so knowing whether we’re in a loop is more valuable than being able to analyze an infinite thing in an infinite way.
This is totally reasonable — but my perspective is:
Not speaking about physical feasibility. I'm working in the theoretical
realm — just as Turing did.
/Flibble
Hi!
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider". It is a Partial Halt Decider over the domain of all *finite* program-input pairs excluding pathological input (a manifestation of the self referencial category error).
It is a Simulating Halt Decider with *infinite resources*.
Turing’s statement of the problem included logically invalid inputs. Once we correct the domain to disallow self-reference, the rest (of *finite*
size) are decidable.
On 4/18/25 5:28 PM, Mr Flibble wrote:
On Fri, 18 Apr 2025 17:15:40 -0400, Richard Damon wrote:
And the rules of the game are that deciders must answer in finite
time.
Your perspective is:
Epistemic: knowledge must be actionable, and thus based on finite
computation.
Pragmatic: we need results in time, so knowing whether we’re in a loop
is more valuable than being able to analyze an infinite thing in an
infinite way.
This is totally reasonable — but my perspective is:
Not speaking about physical feasibility. I'm working in the theoretical
realm — just as Turing did.
/Flibble
But the problems still need the finiteness to have use.
Even in the theoretial, "proof" is still required to be finite, as are deciders.
That is the basic rules of the theoretical system.
On Fri, 18 Apr 2025 19:09:26 -0400, Richard Damon wrote:
On 4/18/25 5:28 PM, Mr Flibble wrote:
On Fri, 18 Apr 2025 17:15:40 -0400, Richard Damon wrote:
And the rules of the game are that deciders must answer in finite
time.
Your perspective is:
Epistemic: knowledge must be actionable, and thus based on finite
computation.
Pragmatic: we need results in time, so knowing whether we’re in a loop >>> is more valuable than being able to analyze an infinite thing in an
infinite way.
This is totally reasonable — but my perspective is:
Not speaking about physical feasibility. I'm working in the theoretical
realm — just as Turing did.
/Flibble
But the problems still need the finiteness to have use.
Even in the theoretial, "proof" is still required to be finite, as are
deciders.
That is the basic rules of the theoretical system.
Theorem (Flibble’s Model-Theoretic Parity Principle):
In any theoretical system that permits infinite computational behavior, a decider analyzing that system may be equipped with equivalent infinite resources, so long as both reside in a consistent meta-model.
/Flibble
Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
[...]
Theorem (Flibble’s Model-Theoretic Parity Principle):
In any theoretical system that permits infinite computational behavior,
a decider analyzing that system may be equipped with equivalent
infinite resources, so long as both reside in a consistent meta-model.
If that's a theorem, what's the proof?
On Sat, 19 Apr 2025 13:00:42 -0700, Keith Thompson wrote:
Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
[...]
Theorem (Flibble’s Model-Theoretic Parity Principle):
In any theoretical system that permits infinite computational behavior,
a decider analyzing that system may be equipped with equivalent
infinite resources, so long as both reside in a consistent meta-model.
If that's a theorem, what's the proof?
Proof of Flibble’s Model-Theoretic Parity Principle:
Theorem (Flibble’s Model-Theoretic Parity Principle)
In any theoretical system S that permits computational entities M to
exhibit unbounded or infinite behavior (e.g., infinite tape, unbounded runtime), it is logically consistent to define an analyzer (decider) D
within an extended system S' with equally unbounded or infinite resources, such that D analyzes M's behavior within the constraints of S, without contradiction — provided S' ⊇ S and D is not subject to stricter constraints than M.
Proof
Let S be a computational system
S allows machines M ∈ S with infinite computational behaviors, such as unbounded tape or unbounded execution time.
Let D be a proposed decider for machines in S
D is designed to determine properties such as halting behavior by
simulating M.
Let S' be an extension of S
S' includes all descriptions and behaviors of S and additionally permits unbounded computational analysis (e.g., infinite simulation time and
memory).
Construction of D
Define D ∈ S' such that D(M, x) simulates M on input x. D may take
infinite steps but is allowed to do so in S'. D returns 'halts' or
'doesn’t halt' based on complete simulation.
Consistency of D
D does not exist in S and does not violate Turing’s Halting Theorem since it operates outside the constraints of S. Turing’s proof applies only to deciders within the same system as the machine they analyze.
Conclusion
Therefore, defining a decider D with equivalent or greater resources than machines M ∈ S is logically consistent, provided D exists in a model S' that extends S and permits such analysis.
/Flibble
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