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. [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.
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Notes
- 1.
A trie representing a finite language L is a tree-like deterministic automaton recognizing L, where the set of states is the set of prefixes of words in L, the initial state is the empty word \(\varepsilon \), the set of final states is a set of sink states, and the set of transitions is \(\{(u,a,ua) {\mid } a \in A\}\).
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Fici, G., Restivo, A., Rizzo, L. (2017). Minimal Forbidden Factors of Circular Words. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_5
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DOI: https://doi.org/10.1007/978-3-319-66396-8_5
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