Learning Weighted Automata over Principal Ideal Domains

TL;DR

This paper investigates active learning algorithms for weighted automata over semirings, demonstrating that a variant of Angluin's \\LStar\\ algorithm is effective over principal ideal domains but not over general semirings like natural numbers.

Contribution

It establishes the applicability of a modified \\LStar\\ algorithm to weighted automata over principal ideal domains, highlighting limitations for other semirings.

Findings

The variant of \\LStar\\ works over principal ideal domains.

The algorithm does not extend to general semirings such as natural numbers.

Provides theoretical boundaries for active learning of weighted automata.

Abstract

In this paper, we study active learning algorithms for weighted automata over a semiring. We show that a variant of Angluin's seminal \LStar\ algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.