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The Point-to-Set Principle in Metric Spaces and Complexity Classes

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SASW09 - International conference on computability, complexity and randomness

The Point-to-Set Principle, which relates the theory of algorithmic information to fractal geometric dimensions, has been a recent avenue for applications of computability theory to geometric measure theory, primarily in Euclidean spaces. In this talk, I will describe two ways that the reach of this principle has been extended. First, it has instances in all separable metric spaces and with respect to more general gauges, permitting a point-to-set analysis of hyperspaces of compact sets, for example. Second, it has resource-bounded instances that can be used to explore the fractal structure of complexity classes. Joint work with Jack H. Lutz and Elvira Mayordomo.

This talk is part of the Isaac Newton Institute Seminar Series series.

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