Maximality and Applications of Subword-Closed Languages

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

Finite language forbidding-enforcing systems

The forbidding and enforcing paradigm was introduced by Ehrenfeucht and Rozenberg as a way to define families of languages based on two sets of boundary conditions. Later, a variant of this paradigm was considered where an fe-system defines a single language. We investigate this variant further by studying fe-systems in which both the forbidding and enforcing sets are finite and show that they define regular languages. We prove that the class of languages defined by finite fe-systems is strictly between the strictly locally testable languages and the class of locally testable languages