Sunday, March 19, 2017

Kolmogorov Complexity

Any random string has inherent complexity and taking the algorithmic complexity approach it is described by kolmogorov complexity. The random string is said to have complexity of K(w) which is given as the length of the shortest program that generates w.
If a program generates a string w has length less than w then kolmogorov complexity of the string is the length of that program. 
We usually have patterns of data taken from our surroundings. Complex processes of physics, chemistry and optics are at play in generation of the patterns that we see around us. Suppose we set out to catalog every pattern of strings generated by computers on the internet. With such a big data its mining would take much time under ordinary circumstances.
Just an image of 100 pixels cross 100 pixels with 8 bits per pixel depth would produce 2 power 80,000 different image combinations.

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