On NFAs Where All States are Final, Initial, or Both

TL;DR

This paper investigates a special class of nondeterministic finite automata where all states are either final, initial, or both, analyzing their computational complexity, language characterization, and state complexity issues.

Contribution

It provides complexity results, language characterizations, and explores state complexity for NFAs with all states final, initial, or both, a novel focus in automata theory.

Findings

Proves hardness of nonuniversality and inequivalence problems for these NFAs.

Characterizes the languages accepted by such automata.

Discusses state complexity problems related to these automata.

Abstract

We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we characterize the languages accepted. Finally, we discuss some state complexity problems involving such automata.