A Survey on Kolmogorov Complexity

Kolmogorov complexity, which is also called algorithmic (descriptive) complexity is an object, such as a piece of text, to measure the computational resources needed, which are mostly the length of the shortest binary program to specify an object. Strings whose Kolmogorov complexity is small relative to the string’s size are not considered to be complex and easy to use a short program to specify it. Based on Kolmogorov complexity, one can easily tell how many and how fast a string can be compressed, which can be measured by resources in time and space such algorithms require. This is especially important nowadays because information is infinity, but process and storage capacity is finite. In this survey, we will get into the definition of Kolmogorov complexity and several applications in several aspects which Kolmogorov complexity is widely used, including efficiency of strategy optimization, security dection and protection and information distance.