6 research outputs found
Avoidability index for binary patterns with reversal
For every pattern over the alphabet , we specify the
least such that is -avoidable.Comment: 15 pages, 1 figur
A family of formulas with reversal of high avoidability index
We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting due to its size and the simple structure of its members. For each k ∈ {4,5}, there are several previously known avoidable formulas (without reversal) of avoidability index k, but they are small in number and they all have rather complex structure.http://dx.doi.org/10.1142/S021819671750024
On the aperiodic avoidability of binary patterns with variables and reversals
In this work we present a characterisation of the avoidability of all unary and binary patterns, that do not only contain variables but also reversals of their instances, with respect to aperiodic infinite words. These types of patterns were studied recently in either more general or particular cases
On avoidability of formulas with reversal
While a characterization of unavoidable formulas (without reversal) is well-known, little
is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas with reversal that have at most two one-way variables (x is a one-way variable in formula with reversal φ if exactly one of x and x^R appears in φ)."This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), grant numbers 418646-2012 and 42410-2010.