Learning Regular Languages over Large Ordered Alphabets

TL;DR

This paper introduces a model for learning regular languages over large or infinite ordered alphabets, extending Angluin's L* algorithm and demonstrating its implementation for numeric alphabets.

Contribution

It proposes a generic automata model with alphabet partitions and extends the L* algorithm to handle large, ordered, and partially ordered alphabets.

Findings

Successfully implemented the extended L* algorithm.

Demonstrated the algorithm on subsets of natural and real numbers.

Outlined potential extensions to partially ordered alphabets.

Abstract

This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the alphabet. We then extend Angluin's L* algorithm for learning regular languages from examples for such automata. We have implemented this algorithm and we demonstrate its behavior where the alphabet is a subset of the natural or real numbers. We sketch the extension of the algorithm to a class of languages over partially ordered alphabets.