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Cellular Automata: Complexity From Simple Rules
A grid of cells, each following a trivial local rule, can generate patterns of endless intricacy.
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Universality: One Machine to Run Them All
A single machine, given the description of any other, can imitate it exactly.
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P Versus NP: The Boundary of the Feasible
Is finding a solution as easy as checking one? For a vast class of problems we can verify an answer quickly but know no fast way to discover it.
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Kolmogorov Complexity: The Length of the Shortest Description
The complexity of an object is the length of the shortest program that produces it.
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Minimum Description Length
The best theory is the one that, together with the data it explains, can be stated most briefly.
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Occam’s Razor: The Case for Simplicity
Faced with rival explanations that fit equally well, prefer the simpler.
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Mutual Information as a Measure of Relationship
How much does knowing one thing tell you about another? The question has a precise answer, a single number that captures dependence of any kind.
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Generative Versus Discriminative: Modeling the World or the Boundary
To tell cats from dogs, one can learn what separates them or learn what each is.