Complexity of proper prefix-convex regular languages

摘要

A language L over an alphabet E is prefix-convex if, for any words x, y, z is an element of Sigma*, 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. (C) 2018 Elsevier B.V. All rights reserved.