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arXiv · 1804.11175

Counting Subwords and Regular Languages

Charles J. Colbourn·Ryan E. Dougherty·Thomas F. Lidbetter·Jeffrey Shallit
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Abstract

Let $x$ and $y$ be words. We consider the languages whose words $z$ are those for which the numbers of occurrences of $x$ and $y$, as subwords of $z$, are the same (resp., the number of $x$'s is less than the number of $y$'s, resp., is less than or equal). We give a necessary and sufficient condition on $x$ and $y$ for these languages to be regular, and we show how to check this condition efficiently.

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Charles J. Colbourn, Ryan E. Dougherty, Thomas F. Lidbetter, Jeffrey Shallit. 2018-06-20. Counting Subwords and Regular Languages. https://arxiv.org/abs/1804.11175

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