On the Representation of Finite Automata

TL;DR

This paper introduces a unique string representation for initially connected deterministic finite automata (ICDFAs), enabling enumeration and exact counting of such automata based on their structure and size.

Contribution

It presents a novel string representation for ICDFAs and a method to generate and count all such automata efficiently.

Findings

Unique string representation for ICDFAs

Method to generate all ICDFAs for given n and k

Enumeration approach for exact counting of ICDFAs

Abstract

We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFAs) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its enumeration provides an alternative way to obtain the exact number of ICDFAs.