Learning Weighted Finite Automata over the Max-Plus Semiring and its Termination

TL;DR

This paper develops an L*-style active learning algorithm for weighted automata over the max-plus semiring, addressing a consistency issue and proving termination for a broad class of languages.

Contribution

It introduces a theoretical fix for the consistency problem in max-plus weighted automata learning and demonstrates termination conditions for the algorithm.

Findings

Identified a consistency failure in existing semiring-generic L* algorithms.

Proposed a mathematically rigorous solution using column-closedness.

Proved termination of the learning algorithm for a broad class of weighted languages.

Abstract

Active learning of finite automata has been vigorously pursued for the purposes of analysis and explanation of black-box systems. In this paper, we study an L*-style learning algorithm for weighted automata over the max-plus semiring. The max-plus setting exposes a "consistency" issue in the previously studied semiring-generic extension of L*: we show that it can fail to maintain consistency of tables, and can thus make equivalence queries on obviously wrong hypothesis automata. We present a theoretical fix by a mathematically clean notion of column-closedness. We also present a nontrivial and reasonably broad class of weighted languages over the max-plus semiring in which our algorithm terminates.