Complexity of Proper Suffix-Convex Regular Languages

TL;DR

This paper investigates the complexity of proper suffix-convex regular languages, introducing a new structural characterization and establishing tight bounds for various automata operations, highlighting the complexity beyond known subclasses.

Contribution

It defines suffix-convex triple systems to characterize automata recognizing proper suffix-convex languages and establishes tight bounds for key operations, advancing understanding of their computational complexity.

Findings

Tight upper bounds for reversal, star, product, and boolean operations.

Introduction of suffix-convex triple systems for automata characterization.

Proof that three witness streams are needed to meet all bounds.

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.