TY - CHAP

T1 - Minimal forbidden factors of circular words

AU - Restivo, Antonio

AU - Fici, Gabriele

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/248542

UR - https://link.springer.com/chapter/10.1007/978-3-319-66396-8_5

M3 - Chapter

SN - 9783319663951

T3 - LECTURE NOTES IN COMPUTER SCIENCE

SP - 36

EP - 48

BT - Combinatorics on Words, 11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings

ER -