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Clark has defined the notion of $n$-avoidance basis which contains theavoidable formulas with at most $n$ variables that are closest to beunavoidable 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 avoidabilityindex 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 most4. We determine exactly the avoidability index of these formulas.

Avoidability of circular formulas