Randomness test
Randomness tests There are many practical measures of randomness for a binary sequence. These include measures based on statistical tests, discrete transforms, and complexity or a mixture of these. These include tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.[1]
These practical tests make it possible to compare and contrast the randomness of strings strings of length 64
0101010101010101010101010101010101010101010101010101010101010101
1100100001100001110111101110110011111010010000100101011110010110
The first string admits a short English language description, namely "32 repetitions of '01'", which consists of 20 characters, and it can be efficiently constructed out of some basis sequences. The second one has no obvious simple description other than writing down the string itself, which has 64 characters, and it has no comparably efficient basis function representation.
Notes
- ^ Terry Ritter, Randomness tests: a literature survey. http://www.ciphersbyritter.com/RES/RANDTEST.HTM