PCA self-assessability?

[hiro-saki]

Could you possibly give a probalbilistically-computing computer like a PCA ( = probabilistic cellular automaton) a function of self-assessments or self-reports to be able to say self-referentially, but, of course, also probabilistically: "I'm making a correct judgment/computation. ( = I'm telling a truth, not a lie.) " ? Please describe the method concretely but roughly/concisely.

Maybe I should re-word the above like:
Could you embed/install a self-debugging meta-PCA into a PCA itself?

[simsim314]

Simplest example but a beat cheating - take a rule where some states are deterministic and some probabilistic. Say you have probabilistic signal that can die out with small probability but a deterministic logical operations on that signal. Now you want to create an output of A and B in form of A&B. You split the signal into several copies and then make sure the outputs match. Of course when you present the output with some signal it might die as well so the output signal is also probabilistic. To reduce probability further the input and the output can consist of several identical copies thus if some of the signal die out - you can have "recovery unit" that takes the majority o input signal and outputs identical copies of it.

[hiro-saki]

Then, could you work any "chaotic" CA as a TM?
The main idea about the above problem is like this:
You meet a total stranger (who may be a villager from The Truths-Tellers Village but who may be a villager from The Liars Village) at a point where the roads to your destination A and to another place branch/fork. So, your question tactics to get the correct direction from the stranger is to ask,
"Do you say: 'Does this road go to A.' ?"
(according to some algorithm theory textbook).
If you can work/use the unreliable stranger to surely give you the truth like that, then likewise, you can work/use the unreliable PCA (or whatever) to perfectly give you the correct answers.

[simsim314]

could you work any "chaotic" CA as a TM?

No. Think of white noise. 0/1 -> {0 (p = 0.5), 1 (p = 0.5)}. No information processing there. In my example I used the fact that it's almost deterministic.

'Does this road go to A.' ?"

There is a bit difference. You can distinguish between consistent and inconsistent answers i.e. random, for example ask the question 10 times. But you can't always distinguish liars from truth tellers as long as both consistent. Anyway you can find the largest city for example.

[hiro-saki]

You are absolutely right! The PCA that can tell that it is telling a lie is The Liar in The Liar Paradox, both of which are unreal/non-existent:

https://forum.wordreference.com/convers ... 506/page-3

But the "randomized algorithms"-producing "randomizing algorithms" only need quasi-random numbers which are actually very orderly, so you must be able to use those "chaotic"algorithms accordingly properly/orderlily.
Thus, it is proven that fools (including randomized/troubled-minded Satan and Satanists wired by God during The Creation) and scissors must get "nice" handlings (including their inevitable eventual eternal Judgements).

[yujh]

You are absolutely right! The PCA that can tell that it is telling a lie is The Liar in The Liar Paradox, both of which are unreal/non-existent:

https://forum.wordreference.com/convers ... 506/page-3

But the "randomized algorithms"-producing "randomizing algorithms" only need quasi-random numbers which are actually very orderly, so you must be able to use those "chaotic"algorithms accordingly properly/orderlily.
Thus, it is proven that fools (including randomized/troubled-minded Satan and Satanists wired by God during The Creation) and scissors must get "nice" handlings (including their inevitable eventual eternal Judgements).

Can’t open the thing it said’log in’

[hiro-saki]

Here is a surrogate/substitute URL for the above broken link:
https://hutschi.wordpress.com/2020/07/12/dm-d-argument/
The Liar Paradox criticism belongs there as a part of it (as part of "Kommentare/commentaries" in English).

[calcyman]

Simplest example but a beat cheating - take a rule where some states are deterministic and some probabilistic. Say you have probabilistic signal that can die out with small probability but a deterministic logical operations on that signal. Now you want to create an output of A and B in form of A&B. You split the signal into several copies and then make sure the outputs match. Of course when you present the output with some signal it might die as well so the output signal is also probabilistic. To reduce probability further the input and the output can consist of several identical copies thus if some of the signal die out - you can have "recovery unit" that takes the majority o input signal and outputs identical copies of it.

Yes! This is one of the ideas behind fault-tolerant quantum computing: if you have a logic gate that makes mistakes with a certain (sufficiently low) probability, you can reduce the error rate by using an error-correcting code (the 'repetition code' you mention being a very simple error-correcting code) and indeed make the error rate arbitrarily small by iterating this idea.

[hiro-saki]

Excuse me: I'm quite a lay-person about this ( = CA) field; I was wondering if you could possibly clarify in plain, every-day English the significance (for the PCAs' UTM-ness problem) of your comment by those technical terms, please.
Or perhaps: do you mean by "arbitrarily small" -- a perfect ZERO, too?

[hiro-saki]

Simplest example but a beat cheating - take a rule where some states are deterministic and some probabilistic. Say you have probabilistic signal that can die out with small probability but a deterministic logical operations on that signal. Now you want to create an output of A and B in form of A&B. You split the signal into several copies and then make sure the outputs match. Of course when you present the output with some signal it might die as well so the output signal is also probabilistic. To reduce probability further the input and the output can consist of several identical copies thus if some of the signal die out - you can have "recovery unit" that takes the majority o input signal and outputs identical copies of it.

Yes! This is one of the ideas behind fault-tolerant quantum computing: if you have a logic gate that makes mistakes with a certain (sufficiently low) probability, you can reduce the error rate by using an error-correcting code (the 'repetition code' you mention being a very simple error-correcting code) and indeed make the error rate arbitrarily small by iterating this idea.

Which do you mean by "arbitrarily small": A. "as small as you wish," or B. "randomly small ( = small but not fixed by any rule)"?
Because the most-detailed dictionary of mine shows these two candidates for the interpretations of "arbitrary" that must be related to your post:
A.: "according to one's wish".
B.: "not fixed by a rule".

[calcyman]

Yes! This is one of the ideas behind fault-tolerant quantum computing: if you have a logic gate that makes mistakes with a certain (sufficiently low) probability, you can reduce the error rate by using an error-correcting code (the 'repetition code' you mention being a very simple error-correcting code) and indeed make the error rate arbitrarily small by iterating this idea.

Which do you mean by "arbitrarily small": A. "as small as you wish," or B. "randomly small ( = small but not fixed by any rule)"?
Because the most-detailed dictionary of mine shows these two candidates for the interpretations of "arbitrary" that must be related to your post:
A.: "according to one's wish".
B.: "not fixed by a rule".

Yes, as small as you wish: http://fab.cba.mit.edu/classes/862.16/n ... n-1956.pdf