… He also showed that the avoidability index of the other formulas in the 3-avoidance basis
is … of the avoidability index of the circular formulas (Theorem 1) and the formulas in the 3-…

… In the rest of the paper, we consider the 2-avoidable formulas in the second part of Theorem
1. Figure 1 gives the maximal length and number of binary words avoiding each maximally 2…

… of studying formulas with reversal of high avoidability index, we … avoidable formulas where
the deletion of any fragment leaves an unavoidable formula, since every avoidable formula …

… We show that the avoidable formulas whose fragments are of the form XY or XY X are 4-…
This includes doubled patterns [12], circular formulas [9], the nice formulas in the 3-avoidance …

… avoidable formula having index 5 or higher. Since f | g implies ind(f) > ind(g). the avoidable
formulas … We show that every circular formula is avoided by Q = 01/21/03/23. The proof is by …

… avoidability index of formulas whose fragments are of the form XY X. The largest avoidability
index of an avoidable … The circular formulas studied in [8] show that AE(f) can be as low as 1 …

… of avoidable formulas with reversal whose avoidability index is unbounded. We also complete
the determination of the avoidability index of the formulas … Avoidability of circular formulas …

… In Chapter 5, we study the avoidability of formulas, a generalization of patterns introduced
… of binary formulas based on the smallest alphabet over which they are avoidable and the …

… exact avoidability index of an avoidable pattern requires more work. Although patterns with
index 4 [2] and 5 [4] have been found, the existence of an avoidable … called circular formulas, …

… In this study, Magic Formula [6] is used as a tire model. Because it is an … right circular
trajectories, and at each state, we must determine which circular trajectory gives a shorter avoidable …