Cheung's theorem

Cheung's theorem concerns the relationship between data compression and randomness. It states that if a data sequence can be compressed significantly, it isn't truly random—since randomness means there's no simpler pattern to describe. Conversely, truly random data can't be compressed much, because it contains maximum unpredictability. Essentially, Cheung's theorem formalizes the idea that the capacity to compress data reflects its level of randomness: highly compressible data is less random, while incompressible data is more random. This connection helps in understanding data complexity, randomness, and the limits of algorithms designed to identify patterns.