An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Conditional complexity and codes
Theoretical Computer Science
IEEE Transactions on Information Theory
Conditional complexity and codes
Theoretical Computer Science
Systems of Strings with High Mutual Complexity
Problems of Information Transmission
Information distance from a question to an answer
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Information shared by many objects
Proceedings of the 17th ACM conference on Information and knowledge management
New information distance measure and its application in question answering system
Journal of Computer Science and Technology
On Generating Independent Random Strings
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Impossibility of independence amplification in Kolmogorov complexity theory
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
SIGACT news complexity theory column 68
ACM SIGACT News
Extracting Kolmogorov complexity with applications to dimension zero-one laws
Information and Computation
Nonapproximability of the normalized information distance
Journal of Computer and System Sciences
Information distance and its applications
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
| Hi-index | 5.23 |
A string p is called a program to compute y given x if U(p,x)=y, where U denotes universal programming language. Kolmogorov complexity K(y|x) of y relative to x is defined as minimum length of a program to compute y given x. Let K(x) denote K(x|emptystring) (Kolmogorov complexity of x) and let I(x:y)=K(x)+K(y)-K(x,y) (the amount of mutual information in x,y). In the present paper, we answer in the negative the following question posed in Bennett et al., IEEE Trans. Inform. Theory 44 (4) (1998) 1407-1423. Is it true that for any strings x,y there are independent minimum length programs p,q to translate between x,y, that is, is it true that for any x,y there are p,q such that U(p,x)=y, U(q,y)=x, the length of p is K(y|x), the length of q is K(x|y), and I(p:q)=0 (where the last three equalities hold up to an additive O(log(K(x|y)+K(y|x))) term)?