Nondeterministic complexity in subclasses of convex languages

Abstract

We study the nondeterministic state complexity of basic regular operations on the classes of prefix-, suffix-, factor-, and subword-free, -closed, and -convex regular languages and on the classes of right, left, two-sided, and all-sided ideal regular languages. For the operations of concatenation, intersection, union, reversal, star, and complementation, we get tight upper bounds for all considered classes except for complementation on factor- and subword-convex languages. Most of our witnesses are described over optimal alphabets. The description of a proper suffix-convex language over a five-letter alphabet meeting the upper bound $2^n$ for complementation, and obtaining an asymptotically tight bound $\mathrm{\Theta }(\sqrt{n})$ for complementation of unary prefix-free languages are among the most interesting results of this paper.