publication . Other literature type . Preprint . 2016

On universal partial words

Chen, Herman Z. Q.; Kitaev, Sergey; Mütze, Torsten; Sun, Brian Y.;
Open Access English
  • Published: 24 Jan 2016
  • Publisher: Episciences.org
Abstract
A universal word for a finite alphabet $A$ and some integer $n\geq 1$ is a word over $A$ such that every word in $A^n$ appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any $A$ and $n$. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from $A$ may contain an arbitrary number of occurrences of a special `joker' symbol $\Diamond\notin A$, which can be substituted by any symbol from $A$. For example, $u=0\Diamond 011100$ is a linear partial word for the binary alphabet $A=\{0,1\}$ and for $n=3$ (e.g., the first three l...
Subjects
arxiv: Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Computer Science::Formal Languages and Automata Theory
free text keywords: Mathematics - Combinatorics, Computer Science - Information Theory, Computer Science - Formal Languages and Automata Theory
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publication . Other literature type . Preprint . 2016

On universal partial words

Chen, Herman Z. Q.; Kitaev, Sergey; Mütze, Torsten; Sun, Brian Y.;