An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
On a definition of random sequences with respect to conditional probability
Information and Computation
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We define monotone complexity ${\textit{KM}}(x,y)$ of a pair of binary strings x,y in a natural way and show that ${\textit{KM}}(x,y)$ may exceed the sum of the lengths of x and y (and therefore the a priori complexity of a pair) by αlog(|x|+|y|) for every αα1). We also show that decision complexity of a pair or triple of strings does not exceed the sum of its lengths.