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arXiv · 1805.11641

Classifying Rotationally-Closed Languages Having Greedy Universal Cycles

Joseph DiMuro
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Abstract

Let $\textbf{T}(n,k)$ be the set of strings of length $n$ over the alphabet $Σ=\{1,2,\ldots,k\}$. A universal cycle for $\textbf{T}(n,k)$ can be constructed using a greedy algorithm: start with the string $k^n$, and continually append the least symbol possible without repeating a substring of length $n$. This construction also creates universal cycles for some subsets $\textbf{S}\subseteq\textbf{T}(n,k)$; we will classify all such subsets that are closed under rotations.

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Joseph DiMuro. 2018-05-29. Classifying Rotationally-Closed Languages Having Greedy Universal Cycles. https://arxiv.org/abs/1805.11641

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