The theory of complexity and entropy of constructive objects

Abstract

The general idea to define complexity of a constructive object as the minimal volume of a program describing this object is due to Kolmogorov (see [Kol 65]). Independently (though in a less explicit form) similar ideas were expressed by Solomonoff in [Sol 64]. In the course of the development of this approach it was found out that different intuitive ideas of complexity correspond to different exact definitions (see, e.g., [Lov 69]). Several attempts to classify different versions of complexity notions can be found in [Lev 76], [Us 92]; the classification given below is based on ideas from [Šen’ 84].