Finding the growth rate of a regular language in polynomial time

TL;DR

This paper presents an efficient algorithm to determine whether a regular language accepted by an automaton has polynomial or exponential growth, and also computes the polynomial degree if applicable.

Contribution

It introduces a polynomial-time algorithm for growth classification of regular languages and an efficient method to determine the polynomial degree for DFA languages.

Findings

Algorithm runs in O(n^3 + n^2 t) time for NFA growth classification.

Quadratic time method to determine polynomial degree for DFA languages.

Provides practical tools for analyzing the complexity of regular languages.

Abstract

We give an O(n^3+n^2 t) time algorithm to determine whether an NFA with n states and t transitions accepts a language of polynomial or exponential growth. We also show that given a DFA accepting a language of polynomial growth, we can determine the order of polynomial growth in quadratic time.