Enumeration of minimal acyclic automata via generalized parking functions

TL;DR

This paper presents an exact counting formula for minimal acyclic deterministic finite automata by establishing a bijection with generalized parking functions, advancing combinatorial enumeration methods.

Contribution

It introduces a novel bijection between generalized parking functions and automata transition functions, enabling precise enumeration of minimal acyclic automata.

Findings

Derived an explicit enumeration formula for minimal acyclic automata

Established a bijection linking parking functions to automata transitions

Enhanced combinatorial understanding of automata structures

Abstract

We give an exact enumerative formula for the minimal acyclic deterministic finite automata. This formula is obtained from a bijection between a family of generalized parking functions and the transitions functions of acyclic automata.