That question makes pretty little sense without fixing some constraints like "what other files exist" and "what language are you allowed to reproduce them".

In a world where every single file is exactly "abcd", it takes zero bits to represent the file - you don't need any information to know that the file contains "abcd" because all files do.

In theory, the language you use to output the file could have a one-bit coding '0' for "produce the file 'there are comments on HN'" (and all other commands starting with '1...'). So in the world we live in, the smallest a file can be compressed to is 1 bit - if you just use the right language.

None of these are practical in general, but the point is that Kolmogorov Complexity is not meaningful without specifying more assumptions/priors.

Absolutely, that is part of what I have come to understand while diving into the topic. That I first needed to answer quite a few other questions for that one to even make sense.

Thank you for the examples; they are much clearer and straightforward than most of those I’ve come across.

This is a misconception. The main result in the Kolmogorov complexity theory that there is precisely the "universal prior" that comes simply from the notion of computability.

It's a misconception the "universal prior" is at all helpful.

This universal prior is both theoretically useful and help conceptualize the real-world compression techniques.

Not to be pedantic, but for any given file the answer is 0% compression, due to the pigeonhole principle.

Not at all! Having basically no knowledge in that area, aside from a vague understanding of the purpose and uses of information theory, it is more than welcome!

For those interested also unfamiliar with it:

- https://eprint.iacr.org/2021/1333.pdf

- https://matt.might.net/articles/why-infinite-or-guaranteed-f...