Complexity of Proper Prefix-Convex Regular Languages
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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.
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Janusz Brzozowski, Corwin Sinnamon (2017). Complexity of Proper Prefix-Convex Regular Languages. UWSpace. http://hdl.handle.net/10012/13158