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math.LO2014
On Reals with -Bounded Complexity and Compressive Power
Ian Herbert
The (prefix-free) Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This gives rise to some `standard' lowness notions for re…
math.LO2014
Lowness for Integer-Valued Randomness
Ian Herbert
A real is called integer-valued random if no integer-valued martingale can win arbitrarily much capital betting against it. A real is low for integer-valued randomness if no intege…
math.LO2012
A Perfect Set of Reals with Finite Self-Information
Ian Herbert
We examine a definition of the mutual information of two reals proposed by Levin. The mutual information is I(X:Y)=log(sum(2^{K(s)-K^X(s)+K(t)-K^Y(t)-K(s,t)}, (s,t) pairs of finite…