### 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.

Original language | English (US) |
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Title of host publication | Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings |

Editors | Mizuho Hoshi, Shinnosuke Seki |

Publisher | Springer Verlag |

Pages | 231-242 |

Number of pages | 12 |

ISBN (Print) | 9783319986531 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 22nd International Conference on Developments in Language Theory, DLT 2018 - Tokyo, Japan Duration: Sep 10 2018 → Sep 14 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11088 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Conference on Developments in Language Theory, DLT 2018 |
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Country | Japan |

City | Tokyo |

Period | 9/10/18 → 9/14/18 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings*(pp. 231-242). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11088 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-98654-8_19

**Counting Subwords and Regular Languages.** / Colbourn, Charles; Dougherty, Ryan E.; Lidbetter, Thomas F.; Shallit, Jeffrey.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11088 LNCS, Springer Verlag, pp. 231-242, 22nd International Conference on Developments in Language Theory, DLT 2018, Tokyo, Japan, 9/10/18. https://doi.org/10.1007/978-3-319-98654-8_19

}

TY - GEN

T1 - Counting Subwords and Regular Languages

AU - Colbourn, Charles

AU - Dougherty, Ryan E.

AU - Lidbetter, Thomas F.

AU - Shallit, Jeffrey

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85053891796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053891796&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-98654-8_19

DO - 10.1007/978-3-319-98654-8_19

M3 - Conference contribution

SN - 9783319986531

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 231

EP - 242

BT - Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings

A2 - Hoshi, Mizuho

A2 - Seki, Shinnosuke

PB - Springer Verlag

ER -