Strategy to locate counterexamples

Tap two blue and one to cast nuh-uh

1. Create any input n
2. Compress n, yielding n₁
3. Compress n₁, yielding n₂
4. Iterate, compressing nₓ, yielding nₓ₊₁, terminating at nₐ

Concept: this compressor does not attempt to achieve infinite compressability. ∴ there is a sequence in the compression of n where compression ceases, which we label nₐ, because Unicode is a jerk and doesn’t have a subscript y or z.

The claim

In essence, this is transforming the question from “is it mathematically possible?” to “can I claim to do it and not being detected as a fraud?”.

The response

No. There is a creatable counterexample at every nₐ.

[pornin]

You might want to read again what you are trying to disclaim. I mean, even the README file! It’s written in plain letter that “this is NOT infinite compression”. I do not (and explain at length in the paper that I cannot) claim to reduce every input, only that that there is no strict increase in length. In your pseudocode, your w_1.length < w_0.length should be w_1.length <= w_0.length.

[StoneCypher]

the issue is that

1. because it isn’t an infinite compressor, there must be a floor
2. if there is a floor, and if it can be found, that constitutes a counterexample
3. the floor can be found through iterated application

On Mon, Oct 4, 2021 at 12:31 PM Solomon Ucko @.***> wrote:

The issue would be that n_(a-1) and n_a are different inputs with the same output?

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