Year
2020
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
Committee Chairperson
Dr. Daniela Genova
Second Advisor
Dr. Michelle DeDeo
Rights Statement
http://rightsstatements.org/vocab/InC/1.0/
Third Advisor
Dr. Jae-Ho Lee
Department Chair
Dr. Richard Patterson
College Dean
Dr. George Rainbolt
Abstract
Characterizing languages D that are maximal with the property that D* ⊆ S⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that the subword closure S⊗ is strictly locally testable. Finally, we discuss applications to coding theory and encoding arbitrary blocks of information on DNA strands. This leads to very important applications in DNA codewords designed to obtain bond-free languages, which have been experimentally confirmed.
Suggested Citation
Jones, Rhys Davis, "Maximality and Applications of Subword-Closed Languages" (2020). UNF Graduate Theses and Dissertations. 978.
https://digitalcommons.unf.edu/etd/978
Included in
Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons, Theory and Algorithms Commons
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