Files ordering + content compression

[CompressMaster]

Hello users,

I need to compress the following set of data:

1.TXT - AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
2.TXT - AAAAAAAAAAAAA
3.TXT - AAAAAAAAAAAAAAAAAAAAAAAAA
4.TXT - AAAAAAAAAAAAA
5.TXT - AAAAAAAAAAAAAAAAAAAAAAAAAAAA
6.TXT - AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAA
7.TXT - AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
and so on...

Description: Each of text file consist of the same character (in this case it´s "A", but it can be replaced with any other symbols from ASCII table) that has been generated RANDOMLY by myself, but it this case randomness will be irrelevant, because it contains only one letter.
Filenames will be ordered descending.

My questions:
1. Since the aforementioned text files will be ordered descending, I suppose that I don´t need to store the filenames at all... it will be given directly from file content. Thus it COULD BE highly compressible, I suppose.
2. What about smart ordering algorithms? I mean: file "2.txt" and "4.txt" contains the same number of symbol, so it can be simplified... but I don´t know how.
3. If "A"´s would causing problems with compression ratio, it is, of course, possible to alter the string with any symbols (interleaving is also possible), but lenght must be preserved as it is.

Thanks a lot.

[Piotr Tarsa]

Compression programs aren't specialized in approaching https://en.wikipedia.org/wiki/Kolmogorov_complexity on weird files. If you have a short generator program then it's probably smaller than output of any conventional file compressor.

Look at: http://mattmahoney.net/dc/#sharnd
If you're able to compress file http://mattmahoney.net/dc/sharnd_challenge.dat so that size of your program plus size of compressed data is smaller than original file then you've basically broken the cryptographic hash algorithm and/ or correctly guessed the input to generator. So far nobody did that and the challenge seems uninteresting, just like your challenges.

[Bulat Ziganshin]

I bet that all these approaches are going around random data compression

[Gotty]

Please read a book.

For example, this:
https://www.amazon.com/dp/1846286026
http://library1.org/_ads/2CB424CF4B5...3F3DBDECF364BB

[Gotty]

I need to compress the following set of data

The questions are as always: how did you generate those files? What do they represent?
And why would you like to compress these files? Are there any practical reasons, or you'd just like to experiment with them?

As I told you earlier in your other threads: we can help you better (or help you at all), if you tell us this information.

If you generate something random, please don't ask us how to compress it. In that case you really must take Shelwien's advice and deepen your knowledge in information theory, and Gonzalo's advice to reread our previous posts with attention.

[CompressMaster]

I need to compress files only for fun. They don´t represent nothing.

OK, so I won´t talk about randomness.