Nondeterministic State Complexity for Suffix-Free Regular Languages

TL;DR

This paper studies the nondeterministic state complexity of fundamental operations on suffix-free regular languages, providing tight bounds for each operation, including a close bound for complementation.

Contribution

It establishes matching upper and lower bounds for the nondeterministic state complexity of key operations on suffix-free regular languages, advancing theoretical understanding.

Findings

Matching bounds for catenation, union, intersection, Kleene star, and reversal.

Near-tight bounds for complementation differing by only two states.

Enhanced understanding of automata complexity for suffix-free languages.

Abstract

We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case for a minimal nondeterministic finite-state automaton that accepts the language obtained from the operation. We consider basic operations (catenation, union, intersection, Kleene star, reversal and complementation) and establish matching upper and lower bounds for each operation. In the case of complementation the upper and lower bounds differ by an additive constant of two.