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arXiv · 1610.04439

Avoidability of circular formulas

Guilhem Gamard·Pascal Ochem·Gwenaël Richomme·Patrice Séébold
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Abstract

Clark has defined the notion of $n$-avoidance basis which contains the avoidable formulas with at most $n$ variables that are closest to be unavoidable in some sense. The family $C_i$ of circular formulas is such that $C_1=AA$, $C_2=ABA.BAB$, $C_3=ABCA.BCAB.CABC$ and so on. For every $i\le n$, the $n$-avoidance basis contains $C_i$. Clark showed that the avoidability index of every circular formula and of every formula in the $3$-avoidance basis (and thus of every avoidable formula containing at most 3 variables) is at most 4. We determine exactly the avoidability index of these formulas.

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Guilhem Gamard, Pascal Ochem, Gwenaël Richomme, Patrice Séébold. 2016-10-14. Avoidability of circular formulas. https://arxiv.org/abs/1610.04439

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