Analyzing monotone space complexity via the switching network model
Name
921854299-MIT.pdf
Description
Full printable version
Size
9.4 MB
Format
Adobe PDF
Checksum (MD5)
2575ff00bf3d27828d7c81b0fa37803b
Author(s)
Potechin, Aaron H
Advisor(s)
Jonathan A. Kelner.
Date Issued
2015
Publisher
Massachusetts Institute of Technology
Abstract
Space complexity is the study of how much space/memory it takes to solve problems. Unfortunately, proving general lower bounds on space complexity is notoriously hard. Thus, we instead consider the restricted case of monotone algorithms, which only make deductions based on what is in the input and not what is missing. In this thesis, we develop techniques for analyzing monotone space complexity via a model called the monotone switching network model. Using these techniques, we prove tight bounds on the minimal size of monotone switching networks solving the directed connectivity, generation, and k-clique problems. These results separate monotone analgoues of L and NL and provide an alternative proof of the separation of the monotone NC hierarchy first proved by Raz and McKenzie. We then further develop these techniques for the directed connectivity problem in order to analyze the monotone space complexity of solving directed connectivity on particular input graphs.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 177-179).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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