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arXiv · 1805.03375

Complexity of Proper Suffix-Convex Regular Languages

Corwin Sinnamon
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Abstract

A language L is suffix-convex if for any words u, v,w, whenever w and uvw are in L, vw is in L as well. Suffix-convex languages include left ideals, suffix-closed languages, and suffix-free languages, which were studied previously. In this paper, we concentrate on suffix-convex languages that do not belong to any one of these classes; we call such languages proper. In order to study this language class, we define a structure called a suffix-convex triple system that characterizes the automata recognizing suffix-convex languages. We find tight upper bounds for reversal, star, product, and boolean operations of proper suffix-convex languages, and we conjecture on the size of the largest syntactic semigroup. We also prove that three witness streams are required to meet all these bounds.

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Corwin Sinnamon. 2018-05-09. Complexity of Proper Suffix-Convex Regular Languages. https://arxiv.org/abs/1805.03375

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