2009/05/14 by Ratsaby, Joel
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.0905.2386
Let |A| denote the cardinality of a finite set A. For any real number x define t(x)=x if x≥1 and 1 otherwise. For any finite sets A,B let δ(A,B) = log2(t(|B∩A||A|)). We define This appears as Technical Report # arXiv:0905.2386v4. A shorter version appears in the Proc. of Mini-Conference on Applied Theoretical Computer Science (MATCOS-10), Slovenia, Oct. 13-14, 2010. a new cobinatorial distance d(A,B) = max\δ(A,B),δ(B,A)\ which may be applied to measure the distance between binary strings of different lengths. The distance is based on a classical combinatorial notion of information introduced by Kolmogorov.