Nonterminal complexity of some families of infinite regular languages

TL;DR

This paper investigates the nonterminal complexity of certain infinite regular languages, providing insights into the minimal grammar size needed to generate these languages, despite the general complexity of the problem.

Contribution

It identifies specific families of infinite regular languages for which nonterminal complexity can be computed, advancing understanding in formal language theory.

Findings

Nonterminal complexity can be computed for certain infinite regular language families.

The paper characterizes the minimal grammars for these language families.

It highlights cases where the complexity problem is solvable despite general unsolvability.

Abstract

Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different families of regular languages. In this paper we study nonterminal complexity of some families of infinite regular languages.