# Counting Subwords and Regular Languages

```@article{Colbourn2018CountingSA,
title={Counting Subwords and Regular Languages},
author={Charles J. Colbourn and Ryan E. Dougherty and Thomas Finn Lidbetter and Jeffrey Shallit},
journal={ArXiv},
year={2018},
volume={abs/1804.11175}
}```
• Published 30 April 2018
• Mathematics
• ArXiv
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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