Proceedings 15th Annual IEEE Conference on Computational Complexity (2000)
July 4, 2000 to July 7, 2000
Andrei Romashchenko , Moscow State University
Nikolai Vereshchagin , Moscow State University
Alexander Shen , Institute of Problems of Information Transmission
The very first Kolmogorov's paper on algorithmic information theory was entitled “Three approaches to the definition of the quantity of information”. These three approaches were called combinatorial, probabilistic and algorithmic. Trying to establish formal connections between combinatorial and algorithmic approaches, we prove that any linear inequality involving Kolmogorov complexities could be translated into an equivalent combinatorial statement.
Kolmogorov complexity, algorithmic information theory, combinatorial inequalities
N. Vereshchagin, A. Shen and A. Romashchenko, "Combinatorial Interpretation of Kolmogorov Complexity," Proceedings 15th Annual IEEE Conference on Computational Complexity(CCC), Florence, Italy, 2000, pp. 131.