Layerwise computability and image randomness

July 14, 2016 · The Ethereal · 🏛 Theory of Computing Systems

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Authors Laurent Bienvenu, Mathieu Hoyrup, Alexander Shen arXiv ID 1607.04232 Category math.LO: Logic Cross-listed cs.IT, math.PR Citations 8 Venue Theory of Computing Systems Last Checked 1 month ago
Abstract
Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only if it has a random preimage. This result (for computable distributions and mappings, and Martin-Löf randomness) was known for a long time (folklore); in this paper we prove its natural generalization for layerwise computable mappings, and discuss the related quantitative results.
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