### Abstract

Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al.ÃÂ [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language M, computes a DFA of the language having M as set of minimal forbidden factors. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We generalize this result to the case of a circular word. We also discuss combinatorial properties of the minimal forbidden factors of a circular word. Finally, we characterize the minimal forbidden factors of the circular Fibonacci words.

Original language | English |
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Title of host publication | Combinatorics on Words, 11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings |

Pages | 36-48 |

Number of pages | 13 |

Publication status | Published - 2017 |

### Publication series

Name | LECTURE NOTES IN COMPUTER SCIENCE |
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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Fici, G., & Restivo, A. (2017). Minimal forbidden factors of circular words. In

*Combinatorics on Words, 11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings*(pp. 36-48). (LECTURE NOTES IN COMPUTER SCIENCE).