Classifying Rotationally-Closed Languages Having Greedy Universal Cycles
Abstract
Let T(n,k)" role="presentation">T(n,k) be the set of strings of length n" role="presentation">n over the alphabet Σ={1,2,…,k}" role="presentation">Σ={1,2,…,k}. A universal cycle for T(n,k)" role="presentation">T(n,k) can be constructed using a greedy algorithm: start with the string kn" role="presentation">kn, and continually append the least symbol possible without repeating a substring of length n" role="presentation">n. This construction also creates universal cycles for some subsets S⊆T(n,k)" role="presentation">S⊆T(n,k); we will classify all such subsets that are closed under rotations.
This paper has been withdrawn.