drummyfish/less_retarded_wiki
5
1
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Update

Browse source
This commit is contained in:
Miloslav Ciz 2023-09-28 17:49:46 +02:00
parent 63f306e93b
commit be8dd746a0
4 changed files with 35 additions and 5 deletions
Download patch file Download diff file Expand all files Collapse all files

27
randomness.md
View file

@ -4,6 +4,33 @@
TODO
## Randomness Tests
TODO
One of the most basic is the **[chi-squared ncept of our measure is following: for given N, we consider a sequence s more random if it gives a lower probability of us correctly predicting the next bit from the subsequencetest](chi_squared_test.md)** whose description can be found e.g. in the *Art of Computer Programming* book. TODO
{ The following is a method I wrote about here (includes some code): https://codeberg.org/drummyfish/my_writings/src/branch/master/randomness.md, I am almost certainly not the first to invent this, but I haven't found what this is called, so for now I'm calling it "my" test, not implying any ownership of course :) If you know what this method is called, please send me a mail. ~drummyfish }
**[Drummyfish's](drummyfish.md) randomness test**: this test tries to measure the unpredictability, the inability to predict what binary digit will follow. As an input to the test we suppose a binary sequence *S* of length *N* bits that's repeating forever (for example for *N = 2* a possible sequence is 10 meaning we are really considering an infinite sequence 1010101010...). We suppose an observer knows the sequence and that it's repeating (consider he has for example been watching us broadcast it for a long time and he noticed we are just repeating the same sequence over and over), then we ask: if the observer is given a random (and randomly long) subsequence *S2* of the main sequence *S*, what's the average probability he can correctly predict the bit that will follow? This average probability is our measured randomness *r* -- the lower the *r*, the "more random" the sequence *S* is according to this test. For different *N* there are different minimum possible values of *r*, it is for example not possible to achieve *r < 0.7* for *N = 3* etc. The following table shows this test's most random sequences for given *N*, along with their count and *r*.
| seq. len. | most random looking sequences |count| min. r |
| --------- | --------------------------------------------------------------------------------------------- | --- | ------ |
| 1 | 0, 1 | 2 | 1.00 |
| 2 | 01, 10 | 2 | 0.50 |
| 3 | 001, 010, 011, 100, 101, 110 | 6 | ~0.72 |
| 4 | 0011, 0110, 1001, 1100 | 4 | ~0.78 |
| 5 | 00101, 01001, 01010, 01011, 01101, 10010, 10100, 10101, 10110, 11010 | 10 | ~0.82 |
| 6 | 000101, 001010, 010001, 010100, 010111, 011101, 100010, 101000, 101011, 101110, 110101, 111010| 12 | ~0.86 |
| 7 | 0001001, 0010001, 0010010, 0100010, 0100100, 0110111, 0111011, 1000100, 1001000, 1011011, ... | 14 | ~0.88 |
| 8 | 00100101, 00101001, 01001001, 01001010, 01010010, 01011011, 01101011, 01101101, 10010010, ... | 16 | ~0.89 |
| 9 | 000010001, 000100001, 000100010, 001000010, 001000100, 010000100, 010001000, 011101111, ... | 18 | ~0.90 |
| 10 | 0010010101, 0010101001, 0100100101, 0100101010, 0101001001, 0101010010, 0101011011, ... | 20 | ~0.91 |
| 11 | 00010001001, 00010010001, 00100010001, 00100010010, 00100100010, 01000100010, 01000100100, ...| 22 | ~0.92 |
| 12 | 001010010101, 001010100101, 010010100101, 010010101001, 010100101001, 010100101010, ... | 24 | ~0.92 |
| 13 | 0010010100101, 0010100100101, 0010100101001, 0100100101001, 0100101001001, 0100101001010, ... | 26 | ~0.93 |
| ... | ... | ... | ... |
## Truly Random Sequence Example
WORK IN PROGRESS { Also I'm not too good at statistics lol. ~drummyfish }