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RESEARCH PRODUCT
Minimal forbidden factors of circular words
Gabriele FiciAntonio RestivoLaura Rizzosubject
FOS: Computer and information sciencesSettore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniGeneral Computer ScienceDiscrete Mathematics (cs.DM)Finite automatonSettore INF/01 - InformaticaFormal Languages and Automata Theory (cs.FL)Factor automatonComputer Science - Formal Languages and Automata TheoryComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Circular wordFibonacci wordMinimal forbidden factorTheoretical Computer ScienceComputer Science::Formal Languages and Automata TheoryComputer Science - Discrete Mathematicsdescription
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 recognizing the language whose set of minimal forbidden factors is $M$. 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 discuss several combinatorial properties of the minimal forbidden factors of a circular word. As a byproduct, we obtain a formal definition of the factor automaton of a circular word. Finally, we investigate the case of minimal forbidden factors of the circular Fibonacci words.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-07-14 |