Incremental construction of minimal acyclic finite-state automata

TL;DR

This paper introduces a novel single-phase method for constructing minimal, deterministic, acyclic finite-state automata directly from a set of strings, improving efficiency over traditional multi-phase approaches.

Contribution

The paper presents a new incremental algorithm that constructs minimal automata in one pass, utilizing on-the-fly minimization and lexicographical ordering of input strings.

Findings

Efficient automaton construction from string sets.

Single-pass incremental algorithm reduces complexity.

Applicable to lexicographically ordered data.

Abstract

In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it. Our approach is to construct a minimal automaton in a single phase by adding new strings one by one and minimizing the resulting automaton on-the-fly. We present a general algorithm as well as a specialization that relies upon the lexicographical ordering of the input strings.