Complexity of proper prefix-convex regular languages

The final publication is available at Elsevier via https://doi.org/10.1016/j.tcs.2018.07.015. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A language L over an alphabet Σ is prefix-convex if, for any words x,y,z ∈ Σ*, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages, which were studied elsewhere. Here we concentrate on prefix-convex languages that do not belong to any one of these classes; we call such languages proper. We exhibit most complex proper prefix-convex languages, which meet the bounds for the size of the syntactic semigroup, reversal, complexity of atoms, star, product, and boolean operations.This work was supported by the Natural Sciences and Engineering Research Council of Canada grant No. OGP0000871