Date of Submission

Spring 2013

Academic Program

Computer Science; Mathematics

Project Advisor 1

James Belk

Project Advisor 2

Robert McGrail

Abstract/Artist's Statement

In this project, we present an efficient implementation of the solution to the conjugacy problem in Thompson's group F, a certain infinite group whose elements are piecewise-linear homeomorphisms of the unit interval [0; 1]. Our algorithm checks for conjugacy by constructing and comparing directed graphs called strand diagrams. We provide a comprehensive description of our solution algorithm, including the data structure we used to hold strand diagrams and the additional subroutines for manipulations of strand diagrams. We prove that our algorithm theoretically achieves an O(n) bound in the size of the input, and we present a O(n2) working solution as an executable JAR file, a web application, and Java source code.

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