
Information Distance Revisited
We consider the notion of information distance between two objects x and...
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On the Algorithmic Probability of Sets
The combined universal probability m(D) of strings x in sets D is close ...
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Exact Expression For Information Distance
Information distance can be defined not only between two strings but als...
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An operational characterization of mutual information in algorithmic information theory
We show that the mutual information, in the sense of Kolmogorov complexi...
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Inequalities for spacebounded Kolmogorov complexity
There is a parallelism between Shannon information theory and algorithmi...
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The Harmonic Edit Distance
This short note introduces a new distance between strings, where the cos...
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Semantic Clone Detection via Probabilistic Software Modeling
Semantic clone detection is the process of finding program elements with...
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Precise Expression for the Algorithmic Information Distance
We consider the notion of information distance between two objects x and y introduced by Bennett, Gács, Li, Vitányi, and Zurek in 1998 as the minimal length of a program that computes x from y as well as computing y from x. In this paper, it was proven that the distance is equal to max (K(xy),K(yx)) up to additive logarithmic terms, and it was conjectured that this could not be improved to O(1) precision. We revisit subtle issues in the definition and prove this conjecture. We show that if the distance is at least logarithmic in the length, then this equality does hold with O(1) precision for strings of equal length. Thus for such strings, both the triangle inequality and the characterization hold with optimal precision. Finally, we extend the result to sets S of bounded size. We show that for each constant s, the shortest program that prints an selement set S ⊆{0,1}^n given any of its elements, has length at most max_w ∈ S K(Sw) + O(1), provided this maximum is at least logarithmic in n.
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