College of Arts and Sciences
Master of Science in Mathematical Sciences (MS)
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
Dr. Daniela Genova
Dr. Michelle DeDeo
Dr. Jae-Ho Lee
Dr. Richard Patterson
Dr. George Rainbolt
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.
Jones, Rhys Davis, "Maximality and Applications of Subword-Closed Languages" (2020). UNF Graduate Theses and Dissertations. 978.