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Author
Title Algorithmic information, fractal geometry, and distributed dynamics
URL
Publication Date
Degree PhD
Discipline/Department Computer Science
Degree Level doctoral
University/Publisher Rutgers University
Abstract

This dissertation applies two distinct algorithmic perspectives to questions in the field of fractal geometry and dynamics. In Part I, we establish connections between algorithmic information theory and classical fractal geometry. Working in Euclidean spaces, we characterize Hausdorff and packing dimensions in terms of relativized Kolmogorov complexity, and we develop conditional dimensions. These tools give rise to new dimensional bounding techniques, which we apply to problems in fractal geometry. Most significantly, we prove that a classical dimension bound for intersections of Borel sets holds for arbitrary sets, and we give a new lower bound on the Hausdorff dimension of generalized Furstenberg sets. In Part II, we use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes interact strategically and with limited information. We exhibit a general non-convergence result for a broad class of dynamics in asynchronous settings. For uncoupled game dynamics, in which preferences are private inputs, we give new bounds on the recall necessary for self stabilization to an equilibrium.

Subjects/Keywords Kolmogorov complexity
Contributors Wright, Rebecca N (chair); Allender, Eric (internal member); Saraf, Shubhangi (internal member); Braverman, Mark (outside member); School of Graduate Studies
Language en
Rights The author owns the copyright to this work.
Country of Publication us
Format 1 online resource (vi, 122 p. : ill.)
Record ID oai:example.org:rutgers-lib:55576
Other Identifiers rutgers-lib:55576; ETD_8228
Repository rutgers
Date Indexed 2019-08-21

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